Representations of quantum toroidal gln
TLDR
In this article, the authors define and study representations of quantum toroidal gl n with natural bases labeled by plane partitions with various conditions, and give an explicit description of a family of highest weight representations for quantum affine gl n.About:
This article is published in Journal of Algebra.The article was published on 2013-04-15 and is currently open access. It has received 63 citations till now.read more
Citations
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Quantum geometry and quiver gauge theories
TL;DR: In this paper, the universal part of the effective twisted superpotential of the quiver gauge theory was derived for a d-dimensional torus and a two-dimensional cigar with the same deformation.
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Explicit examples of DIM constraints for network matrix models
Hidetoshi Awata,Hiroaki Kanno,Takuya Matsumoto,Andrei Mironov,Alexei Morozov,Alexei Morozov,Andrey Morozov,Andrey Morozov,Yusuke Ohkubo,Yegor Zenkevich,Yegor Zenkevich +10 more
TL;DR: In this paper, Dotsenko-Fateev and Chern-Simons matrix models are incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry, and the Ward identities are also promoted to the DIM level, where they all become corollaries of a single identity.
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Branching rules for quantum toroidal gln
TL;DR: In this article, an analog of the subalgebra U gl ( n ) ⊗ U gl m ⊂ U gl n + n was constructed in the setting of quantum toroidal algebras.
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Coproduct for Yangians of affine Kac–Moody algebras
TL;DR: In this article, a coproduct on affine Kac-Moody algebras is constructed and shown to be an algebra homomorphism, and a minimalistic presentation of the Yangian is given when the kac-moody algebra is symmetrizable.
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( q, t )-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
Hidetoshi Awata,Hiroaki Kanno,Andrei Mironov,Alexei Morozov,Alexei Morozov,Kazuma Suetake,Yegor Zenkevich,Yegor Zenkevich,Yegor Zenkevich +8 more
TL;DR: In this article, the Wess-Zumino-Witten model was lifted from the level of one-loop Kac-Moody to generic quantum toroidal algebras.
References
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A (q,γ) analog of the W1+∞ algebra
TL;DR: In this paper, a (q,γ)-approximation of the W1+∞ algebra is introduced and a tensor matrices acting on the tensor product of these modules is investigated.
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Langlands Reciprocity for Algebraic Surfaces
TL;DR: In this article, the authors extend the geometric Langlands conjecture from algebraic curves to algebraic surfaces and show that the algebra generated by the Hecke operators turns out to be a homomorphic image of quantum toroidal algebra.
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Quantum continuous $\mathfrak{gl}_\infty$: Semi-infinite construction of representations
TL;DR: In this article, the authors studied the representation theory of quantum continuous Laplace polynomials in one variable, and constructed a tensor product of vector representations to spherical double affine Hecke algebras.
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Quantum continuous $\mathfrak{gl}_{\infty}$: Semiinfinite construction of representations
TL;DR: In this paper, the authors studied the representation theory of quantum continuous gl∞, which is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable.
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Schur duality in the toroidal setting
Michela Varagnolo,E. Vasserot +1 more
TL;DR: In this article, the authors extend the classical Frobenius-Schur duality to the quantum toroidal setup with only algebraic methods, and show that the representations involved in the duality are infinite dimensional.