A $(q, t)$-deformation of the 2d Toda integrable hierarchy (Q6593158)

scientific article; zbMATH DE number 7901677

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English	A $(q, t)$-deformation of the 2d Toda integrable hierarchy	scientific article; zbMATH DE number 7901677

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title

A $(q, t)$-deformation of the 2d Toda integrable hierarchy (English)

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Communications in Mathematical Physics

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publication date

26 August 2024

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Toda lattice hierarchy and conservation laws

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Toda hierarchies and their applications

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Solitons and infinite dimensional Lie algebras

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Multivariate hypergeometric functions as $\tau$-functions of Toda lattice and Kadomtsev-Petviashvili equation

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Time-dependent backgrounds of 2D string theory

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Toda equations for Hurwitz numbers

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ABJM matrix model and 2D Toda lattice hierarchy

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Topological strings and integrable hierarchies

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Melting crystal, quantum torus and Toda hierarchy

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Link homologies and the refined topological vertex

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

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Quantum algebraic approach to refined topological vertex

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Ding-Iohara-Miki symmetry of network matrix models

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Explicit examples of DIM constraints for network matrix models

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

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A (q,γ) analog of the W1+∞ algebra

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Intertwining operator and integrable hierarchies from topological strings

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$q$-Painlevé VI equation arising from $q$-UC hierarchy

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FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS

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Conformal field theory of Painlevé VI

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Liouville correlation functions from four-dimensional gauge theories

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CFT approach to the q-Painlevé VI equation

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Five-dimensional AGT conjecture and the deformed Virasoro algebra

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Cluster integrable systems, $q$-Painlevé equations and their quantization

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Non-stationary difference equation and affine Laumon space: quantization of discrete Painlevé equation

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Affine screening operators, affine Laumon spaces and conjectures concerning non-stationary Ruijsenaars functions

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Non-stationary Ruijsenaars functions for $\kappa = t^{-1/N}$ and intertwining operators of Ding-Iohara-Miki algebra

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

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Finite type modules and Bethe ansatz for quantum toroidal $\mathfrak{gl}_1$

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KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–

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Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–

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Q3032461

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Free fermions and tau-functions

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Q4939475

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A commutative algebra on degenerate CP1 and Macdonald polynomials

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Equivariant $K$-theory of Hilbert schemes via shuffle algebra

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

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

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Liouville reflection operator, affine Yangian and Bethe ansatz

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Vertex operator representation of some quantum tori Lie algebras

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A note on the S-dual basis in the free fermion system

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Quantum W1+∞ subalgebras of BCD type and symmetric polynomials

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Q4830310

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Fiber-base duality from the algebraic perspective

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Interpretations of some parameter dependent generalizations of classical matrix ensembles

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Macdonald processes

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Quantum spectral curve for $(q,t)$-matrix model

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Solving $q$-Virasoro constraints

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b-Monotone Hurwitz Numbers: Virasoro Constraints, BKP Hierarchy, andO(N)-BGW Integral

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The Shuffle Algebra Revisited

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The $R$-matrix of the quantum toroidal algebra

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Bethe subalgebras of $U_q(\widehat{\mathfrak{gl}}_n)$ via shuffle algebras

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The Maulik–Okounkov R-matrix from the Ding–Iohara–Miki algebra

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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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Computing the R-matrix of the quantum toroidal algebra

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Quantum groups and quantum cohomology

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

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On the instanton $R$-matrix

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Classical tau-function for quantum spin chains

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The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function

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The master $T$-operator for the Gaudin model and the KP hierarchy

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On the Hall algebra of an elliptic curve. I.

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Stable maps, Q-operators and category 𝒪

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$(q, t)$-deformed (skew) Hurwitz $\tau$-functions

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Integrability of Hurwitz partition functions

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On KP-integrable skew Hurwitz $\tau$-functions and their $\beta$-deformations

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

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Shifted quantum groups and matter multiplets in supersymmetric gauge theories

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Quiver W-algebras

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Identifiers

Mathematics Subject Classification ID

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10.1007/S00220-024-05076-6

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Sitelinks

Mathematics(1 entry)

mardi Publication:6593158

A \((q, t)\)-deformation of the 2d Toda integrable hierarchy (Q6593158)

Statements

Identifiers

Sitelinks

Mathematics(1 entry)