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

DOI10.1007/BF02102595zbMath0873.17016arXivq-alg/9508011OpenAlexW1869847189MaRDI QIDQ1924050

Harunobu Kubo, Hidetoshi Awata, Satoru Odake, Jun'ichi Shiraishi

Publication date: 30 October 1997

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9508011

zbMATH Keywords

singular vectors vertex operators quantum Miura transformation general Macdonald polynomials quantum $W_ N$ algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Vertex operators; vertex operator algebras and related structures (17B69) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (73)

NSR singular vectors from Uglov polynomials ⋮ $q$-Virasoro modular double and 3d partition functions ⋮ Fractional quiver W-algebras ⋮ ℏ (YANGIAN) DEFORMATION OF THE MIURA MAP AND VIRASORO ALGEBRA ⋮ Free field approach to the dilute AL models ⋮ Combinatorics of vertex operators and deformed $W$-algebra of type D$(2,1;\alpha)$ ⋮ Symmetry enhancements via 5d instantons, $ q\mathcal{W} $-algebrae and $(1,0)$ superconformal index ⋮ Quiver ${\text{W}}_{{\boldsymbol{{\epsilon}}}_{\mathbf{1}},{\boldsymbol{{\epsilon}}}_{\mathbf{2}}}$ algebras of 4D $\boldsymbol{\mathcal{N}}\mathbf{=}\mathbf{2}$ gauge theories ⋮ Supersymmetric Wilson loops, instantons, and deformed $\mathcal{W}$-algebras ⋮ COMMENTS ON THE DEFORMED W_N ALGEBRA ⋮ A note on the deformed Virasoro algebra ⋮ Form-factors of exponential fields in the affine $A^{(1)}_{N-1}$ Toda model ⋮ Lattice $W_N$ algebra and its quantization ⋮ Five-dimensional AGT conjecture and the deformed Virasoro algebra ⋮ Deformed Virasoro algebras from elliptic quantum algebras ⋮ Quantum geometry and quiver gauge theories ⋮ An elliptic Virasoro symmetry in 6d ⋮ On quiver W-algebras and defects from gauge origami ⋮ Dynamical centers for the elliptic quantum algebra $ \newcommand{\elpb}[1{{{\mathcal{B}}_{q,\lambda}(\widehat{gl}_{#1})_c}} \newcommand{\e}{{\rm e}} \elpb{2}$] ⋮ W$W$‐algebras associated to surfaces ⋮ AGT relations for sheaves on surfaces ⋮ $q$-Virasoro/$W$ algebra at root of unity and parafermions ⋮ Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra, and 5D AGT correspondence ⋮ Holomorphic blocks and the 5d AGT correspondence ⋮ The integrals of motion for the elliptic deformation of the Virasoro and algebra ⋮ Elliptic modular double and 4d partition functions ⋮ 5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_1$ ⋮ Elliptic algebra, Frenkel–Kac construction and root of unity limit ⋮ The $q$-AGT-W relations via shuffle algebras ⋮ Elliptic quantum toroidal algebra $U_{q,t,p}(\mathfrak{gl}_{1,tor})$ and affine quiver gauge theories ⋮ 2d-4d connection between $q$-Virasoro/$W$ block at root of unity limit and instanton partition function on ALE space ⋮ Poisson structures on the center of the elliptic algebra $\mathcal A_{q,p}(\widehat{\text{sl}}(2)_c)$ ⋮ New $\mathcal W_{q,p}(\text{sl}(2))$ algebras from the elliptic algebra $\mathcal A_{q,p}(\widehat{\text{sl}}(2)_c)$ ⋮ Central extensions of classical and quantum $q$-Virasoro algebras ⋮ Double quantization of Seiberg–Witten geometry and W-algebras ⋮ Elliptic Ding-Iohara algebra and the free field realization of the elliptic Macdonald operator ⋮ A (q,γ) analog of the W1+∞ algebra ⋮ Kac determinant and singular vector of the level $N$ representation of Ding-Iohara-Miki algebra ⋮ Matrix model from $ \mathcal{N} = 2 $ orbifold partition function ⋮ Quantum $q$-Langlands Correspondence ⋮ $q$-Virasoro modular triple ⋮ 3d and 5d gauge theory partition functions as $q$-deformed CFT correlators ⋮ G-equivariant ϕ-coordinated quasi modules for quantum vertex algebras ⋮ “Composite particles” and the eigenstates of Calogero–Sutherland and Ruijsenaars–Schneider ⋮ Quantum geometry and $\theta$-angle in five-dimensional super Yang-Mills ⋮ The integrals of motion for the deformed $W$-algebra $W_{q,t}(\widehat{gl_N})$. II: Proof of the commutation relations ⋮ A probabilistic interpretation of the Macdonald polynomials ⋮ A commutative algebra on degenerate CP1 and Macdonald polynomials ⋮ Angular quantization and form factors in massive integrable models ⋮ An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity ⋮ Angular quantization and form factors in massive integrable models ⋮ On the quantization of Seiberg-Witten geometry ⋮ $q$-deformation of corner vertex operator algebras by Miura transformation ⋮ Singular vectors of the Ding-Iohara-Miki algebra ⋮ Deformations of $\mathcal{W}$ algebras via quantum toroidal algebras ⋮ The ABCDEFG of little strings ⋮ REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS ⋮ Deformed $W$-algebras in type $A$ for rectangular nilpotent ⋮ Elliptic quantum group $U_{q,p}(\widehat{\mathfrak{sl}}_2)$, Hopf algebroid structure and elliptic hypergeometric series ⋮ On elliptic algebras and large-n supersymmetric gauge theories ⋮ An algebraic approach to the non-symmetric Macdonald polynomial ⋮ Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1)) ⋮ Quadratic relations of the deformed $W$-algebra for the twisted affine Lie algebra of type $A_{2N}^{(2)}$ ⋮ The algebra ${\mathcal A}_{\hbar,\eta}(\hat g)$ and infinite Hopf family of algebras ⋮ An Ar threesome: Matrix models, 2d conformal field theories, and 4d N=2 gauge theories ⋮ A note on quiver quantum toroidal algebra ⋮ Shifted quiver quantum toroidal algebra and subcrystal representations ⋮ TYPE II VERTEX OPERATORS FOR THE $\bm{A_{\lc{n}-1}^{(1)}}$ FACE MODEL ⋮ Cubic constraints for the resolvents of the ABJM matrix model and its cousins ⋮ Elliptic algebra $U_{q,p}(\hat{\mathfrak {g}})$ and quantum $Z$-algebras ⋮ A slow review of the AGT correspondence ⋮ On $q$-deformed infinite-dimensional $n$-algebra ⋮ Quadratic relations of the deformed W-superalgebra Wq,tA(M,N)

Cites Work

This page was built for publication: Quantum ${\mathcal W}_ N$ algebras and Macdonald polynomials

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