Quantum toroidal algebras and solvable structures in gauge/string theory (Q6497323)

scientific article; zbMATH DE number 7842936

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English	Quantum toroidal algebras and solvable structures in gauge/string theory	scientific article; zbMATH DE number 7842936

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title

Quantum toroidal algebras and solvable structures in gauge/string theory (English)

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6 May 2024

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zbMATH Keywords

quantum toroidal algebra

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string theory

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supersymmetric theory

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conformal field theory

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integrable models

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MaRDI profile type

MaRDI publication profile

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cites work

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Geometric engineering of quantum field theories

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Mirror symmetry and exact solution of $4D$ $N=2$ gauge theories. I

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Quantum algebraic approach to refined topological vertex

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Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz

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Quantum groups and quantum cohomology

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Instanton R-matrix and $\mathcal{W}$-symmetry

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Yang-Mills instantons on ALE gravitational instantons

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The elliptic Hall algebra and the $K$-theory of the Hilbert scheme of $\mathbb{A}^{2}$

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New quantum toroidal algebras from 5D $\mathcal{N} = 1$ instantons on orbifolds

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Crystal melting and toric Calabi-Yau manifolds

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Brane tilings and their applications

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On the algebras of BPS states.

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Crystal melting, BPS quivers and plethystics

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Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants

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On cohomological Hall algebras of quivers: generators

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Schur duality in the toroidal setting

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Macdonald's evaluation conjectures and difference Fourier transform

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Double affine Hecke algebras and Macdonald's conjectures

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Lectures on affine Hecke algebras and Macdonald’s conjectures

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Drinfeld realization of the elliptic Hall algebra

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Geometric representations of graded and rational Cherednik algebras

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A Presentation of the Deformed W 1+∞ Algebra

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Spherical Hecke algebra in the Nekrasov-Shatashvili limit

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Quantum toroidal $\mathfrak{gl}_{1}$-algebra: plane partitions

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Quantum continuous $\mathfrak{gl}_{\infty}$: tensor products of Fock modules and $\mathcal{W}_{n}$-characters

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A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

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Quantum ${\mathcal W}_ N$ algebras and Macdonald polynomials

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Quantum ${\mathcal W}$-algebras and elliptic algebras

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Magnificent four

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Magnificent four with colors

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$3d$ field theory, plane partitions and triple Macdonald polynomials

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Quantum affine algebras and deformations of the Virasoro and ${\mathcal W}$-algebras

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COMMENTS ON THE DEFORMED WN ALGEBRA

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Deformations of $\mathcal{W}$ algebras via quantum toroidal algebras

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$(p,q)$-webs of DIM representations, 5d $\;\mathcal{N}=1 $ instanton partition functions and qq-characters

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Plane partition realization of (web of) $ \mathcal{W} $-algebra minimal models

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Restricted partition pairs

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AGT, $N$-Burge partitions and $ {\mathcal{W}}_N $ minimal models

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Cylindric Partitions

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Cylindric partitions, ${{\boldsymbol{ \mathcal W }}}_{r}$ characters and the Andrews–Gordon–Bressoud identities

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THE STRUCTURE OF REPRESENTATION FOR THE W(3) MINIMAL MODEL

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The supersymmetric affine Yangian

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Twin-plane-partitions and $ \mathcal{N} =2$ affine Yangian

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Integrable structure of conformal field theory. III: The Yang-Baxter relation

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Yangian associated with 2D𝒩= 1 SCFT

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The $R$-matrix of the quantum toroidal algebra $U_{q,t}(\overset{..}{gl}_1)$ in the Fock module

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Liouville reflection operator, affine Yangian and Bethe ansatz

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Conformal blocks in Virasoro and W theories: Duality and the Calogero-Sutherland model

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Towards the proof of AGT relations with the help of the generalized Jack polynomials

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On spectrum of ILW hierarchy in conformal field theory II: coset CFT's

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Excited states in some simple perturbed conformal field theories

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Higher-level eigenvalues of $Q$-operators and Schrödinger equation

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On elliptic algebras and large-n supersymmetric gauge theories

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The Shuffle Algebra Revisited

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Instantons from blow-up

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Wall-crossing, Hitchin systems, and the WKB approximation

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General Argyres-Douglas theory

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The Self-Duality Equations on a Riemann Surface

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Reading between the lines of four-dimensional gauge theories

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Instanton moduli spaces and $\mathscr W$-algebras

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Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial

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Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

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Refined topological strings on local $\mathbb P^2 $

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Instanton Counting, Quantum Geometry and Algebra

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Spiked instantons from intersecting D-branes

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BPS/CFT correspondence. II: Instantons at crossroads, moduli and compactness theorem

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BPS/CFT correspondence. III: Gauge origami partition function and $qq$-characters

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BPS/CFT correspondence. IV: Sigma models and defects in gauge theory

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Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d super Yang–Mills

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Thermodynamic limit of Nekrasov partition function for 5-brane web with $O5$-plane

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Integrability and Seiberg-Witten exact solution

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Integrable systems and supersymmetric gauge theory

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Supersymmetric Yang-Mills theory and integrable systems

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2d partition function in $\Omega$-background and vortex/instanton correspondence

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Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants

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Deformed prepotential, quantum integrable system and Liouville field theory

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On the Hall algebra of an elliptic curve. II

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The Hall algebra of a curve

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Q4981649

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Hall algebras and quantum groups

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Hall algebras, hereditary algebras and quantum groups

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Drinfeld double and Ringel-Green theory of Hall algebras

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Q3840129

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A commutative algebra on degenerate CP1 and Macdonald polynomials

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Quantum toroidal and shuffle algebras

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The $q$-AGT-W relations via shuffle algebras

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Quiver elliptic W-algebras

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Fractional quiver W-algebras

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Integrating over quiver variety and BPS/CFT correspondence

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Double quiver gauge theory and BPS/CFT correspondence

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Trialities of orthosymplectic $\mathcal{W} $-algebras

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Orbifolds of Gaiotto-Rapčák $Y$-algebras

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Branching rules for quantum toroidal $\mathfrak{gl}_n$

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The MacMahon R-matrix

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Mixed network calculus

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Engineering 3D $\mathcal{N} = 2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra

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Shifted quantum groups and matter multiplets in supersymmetric gauge theories

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Macmahon KZ equation for Ding-Iohara-Miki algebra

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Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

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Web construction of ABCDEFG and affine quiver gauge theories

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ABCD of instantons

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Instanton counting and O-vertex

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Recursive method for the Nekrasov partition function for classical Lie groups

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On the Jeffrey–Kirwan residue ofBCD-instantons

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From SO/Sp instantons to W-algebra blocks

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ABCD of qq-characters

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The ABCDEFG of instantons and W-algebras

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5-brane webs for 5d $ \mathcal{N}=1 \;$ $G_2$ gauge theories

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Rank-3 antisymmetric matter on 5-brane webs

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More on topological vertex formalism for 5-brane webs with O5-plane

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Topological vertex for 6d SCFTs with $\mathbb{Z}_2$-twist

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Refined topological vertex with ON-planes

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5d/6d DE instantons from trivalent gluing of web diagrams

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6d/5d exceptional gauge theories from web diagrams

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Negative branes, supergroups and the signature of spacetime

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Ghost D-branes

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Intersecting defects and supergroup gauge theory

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Topological vertex/anti-vertex and supergroup gauge theory

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5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_1$

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Braid actions on quantum toroidal superalgebras

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$(q, t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces

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A note on the algebraic engineering of 4D $\mathcal{N} = 2$ super Yang-Mills theories

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An elliptic vertex of Awata-Feigin-Shiraishi type for M-strings

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An elliptic topological vertex

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$4d$ Higgsed network calculus and elliptic DIM algebra

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Quasi-Hopf twist and elliptic Nekrasov factor

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Elliptic quantum toroidal algebra $U_{q,t,p}(\mathfrak{gl}_{1,tor})$ and affine quiver gauge theories

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Quantum toroidal algebras and their vertex representations

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Toroidal actions on level 1 modules of $U_q(\widehat{sl}_n)$

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Quantum toroidal algebra Uq(sl2,tor) and R matrices

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Quantum toroidal algebras and their representations

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Several realizations of Fock modules for toroidal $\ddot {U}_{q,d}(\mathfrak {sl}_{n})$

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Affine Yangian action on the Fock space

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Affine Yangian of $\mathfrak{gl}(2)$ and integrable structures of superconformal field theory

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R-matrix formulation of affine Yangian of $\widehat{\mathfrak{gl}}(1|1)$

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Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian

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A note on quiver Yangians and $\mathcal{R}$-matrices

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Opers, surface defects, and Yang-Yang functional

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TOROIDAL q-OPERS

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Riemann-Hilbert correspondence and blown up surface defects

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Quantum affine algebras and holonomic difference equations

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Anomaly in $\mathcal{RTT}$ relation for DIM algebra and network matrix models

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Surface defects in gauge theory and KZ equation

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Q3715293

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Degenerate affine Hecke algebras and Yangians

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Q5749435

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Q5749433

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Q3351551

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Yang-Baxter equation and representation theory. I

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Some algebraic structures connected with the Yang-Baxter equation

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A $q$-analogue of $U(\mathfrak{gl}(N+1))$, Hecke algebra, and the Yang-Baxter equation

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Q4321790

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From quantum loop algebras to Yangians

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Yangians and quantum loop algebras

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Coproduct for Yangians of affine Kac-Moody algebras

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Affine Hecke algebras and raising operators for Macdonald polynomials

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Vertex operators and Hall-Littlewood symmetric functions

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A formula for two-row Macdonald functions

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Algebraic structures and eigenstates for integrable collective field theories

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$q$-hypergeometric series and Macdonald functions

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Integral representations of the Macdonald symmetric polynomials

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Generalized Macdonald functions on Fock tensor spaces and duality formula for changing preferred direction

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Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials

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REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.PHYSREP.2023.12.003

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Sitelinks

Mathematics(1 entry)

mardi Publication:6497323