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

DOI10.1007/BF01237841zbMath0915.17012arXivq-alg/9702024MaRDI QIDQ1383881

Denis Uglov, Yoshihisa Saito, Kouichi Takemura

Publication date: 5 July 1999

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9702024

zbMATH Keywords

highest weight modulesFock spacevertex representationquantum toroidal algebraaffine quantum algebraquantum toroidal action

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

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Cites Work

• Schur duality in the toroidal setting
• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• A new interpretation of Gelfand-Tsetlin bases
• Double-loop algebras and the Fock space
• Level-0 action of \(U_q(\widehat{\mathfrak sl}_n)\) on the \(q\)-deformed Fock spaces
• Staggered polarization of vertex models with \(U_ q(\widehat {sl}(n))\)- symmetry
• Spinons in conformal field theory
• Double affine Hecke algebras and Macdonald's conjectures
• Langlands reciprocity for algebraic surfaces
• Decomposition of \(q\)-deformed Fock spaces
• Semi-infinite wedges and the conformal limit of the fermionic Calogero-Sutherland model with spin \(1\over 2\)
• Quantum affine algebras and affine Hecke algebras
• Level-0 structure of level-1 U_q(sl₂)-modules and Macdonald polynomials