Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations
type: Item
instance of: scholarly article
title: Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations
author: Hitoshi Konno
author: Kazuyuki Oshima
published in: Algebras and Representation Theory
publication date: 2024-05-10T00:00:00Z
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7845594
MaRDI profile type: Publication
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cites work: Anomaly in \(\mathcal{RTT}\) relation for DIM algebra and network matrix models
cites work: \((q, t)\)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
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cites work: Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d super Yang–Mills
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cites work: Q3819193
cites work: Q3819194
cites work: Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
cites work: Exchange dynamical quantum groups
cites work: Elliptic algebra \(U_{q,p}(\hat{\mathfrak {g}})\) and quantum \(Z\)-algebras
cites work: Quantum continuous \(\mathfrak{gl}_{\infty}\): semiinfinite construction of representations
cites work: Quantum continuous \(\mathfrak{gl}_{\infty}\): tensor products of Fock modules and \(\mathcal{W}_{n}\)-characters
cites work: Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra
cites work: Verma modules over the Virasoro algebra
cites work: Quantum toroidal \(\mathfrak{gl}_{1}\)-algebra: plane partitions
cites work: Representations of quantum toroidal \(\mathfrak{gl}_n\)
cites work: Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz
cites work: Branching rules for quantum toroidal \(\mathfrak{gl}_n\)
cites work: Evaluation modules for quantum toroidal \(\mathfrak{gl}_n\) algebras
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cites work: Vertex representations of quantum affine algebras
cites work: Deformations of \(W\)-algebras associated to simple Lie algebras
cites work: Langlands reciprocity for algebraic surfaces
cites work: Unitary representations of the Virasoro and super-Virasoro algebras
cites work: Quantum toroidal algebras and their representations
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: Free field construction for the ABF models in regime II.
cites work: Elliptic algebra \(U_{q,p} (\widehat {\mathfrak {sl}}_2)\): Drinfeld currents and vertex operators
cites work: Quasi-Hopf twistors for elliptic quantum groups
cites work: Q4323298
cites work: Higher level representations of the quantum affine algebra \(U_ q(\hat sl(2))\)
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cites work: Elliptic quantum toroidal algebra \(U_{q,t,p}(\mathfrak{gl}_{1,tor})\) and affine quiver gauge theories
cites work: Q3320568
cites work: A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
cites work: The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
cites work: Q4632223
cites work: Quantum groups and quantum cohomology
cites work: Toroidal braid group action and an automorphism of toroidal algebra \(U_q(sl_{n+1,\text{tor}})\) \((n\geqq 2)\)
cites work: Toroidal and level 0 Uq′(sln+1∧) actions on Uq(gln+1∧) modules
cites work: Representations of quantum toroidal algebra \(U_q(\text{sl}_{n+1,\text{tor}}) (n\geq 2)\)
cites work: A (q,γ) analog of the W1+∞ algebra
cites work: Quiver varieties and finite dimensional representations of quantum affine algebras
cites work: \(K\)-theory of quiver varieties, \(q\)-Fock space and nonsymmetric Macdonald polynomials
cites work: The Shuffle Algebra Revisited
cites work: The \(q\)-AGT-W relations via shuffle algebras
cites work: Seiberg-Witten prepotential from instanton counting
cites work: BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and \(qq\)-characters
cites work: An elliptic Virasoro symmetry in 6d
cites work: Elliptic hypergeometric series on root systems.
cites work: Quantum toroidal algebras and their vertex representations
cites work: Toroidal actions on level 1 modules of \(U_q(\widehat{sl}_n)\)
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Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations (DOI)
DOI: 10.1007/S10468-024-10251-3