Introduction to Quantum Groups

Lusztig, G.

doi:10.1007/978-0-8176-4717-9

Cited by 992 publications

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“…The quantum version of the Gabber-Kac theorem says that I is generated by these elements over all pairs of vertices i = j of the graph Γ (for instance, see Theorem 33.1.3 in [34]). …”

Section: Proposition 32 [Res] Is An Algebra Homomorphism Frommentioning

confidence: 99%

A diagrammatic approach to categorification of quantum groups I

2009

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“…The quantum version of the Gabber-Kac theorem says that I is generated by these elements over all pairs of vertices i = j of the graph Γ (for instance, see Theorem 33.1.3 in [34]). …”

Section: Proposition 32 [Res] Is An Algebra Homomorphism Frommentioning

confidence: 99%

A diagrammatic approach to categorification of quantum groups I

2009

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“…e.g. [73] [103]) is obtained as the (generic, twisted) Ringel-Hall algebra of the abelian category of finite-dimensional representations of a quiver ∆ with underlying graph ∆. After Ringel's discovery, it was first pointed out by Xiao [165], cf.…”

Section: 5mentioning

confidence: 99%

Differential graded categories

Tabuada¹

2015

University Lecture Series

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“…Even in the non-graded case of quantum affine algebras considered in [15], the integrability property (Theorem 2.1) is non-trivial (see the references therein). (2) From integrability, we get an action of Weyl group on the set P of weights [35,Sect. 41.2].…”

Section: Remark 411 (1) Our Proof Relied Heavily On the Theory Of Wementioning

confidence: 99%

Representations of quantum affine superalgebras

Zhang

2014

Math. Z.

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We study the quantum affine superalgebra U q (Lsl(M, N )) and its finitedimensional representations. We prove a triangular decomposition and establish a system of Poincaré-Birkhoff-Witt generators for this superalgebra, both in terms of Drinfel'd currents. We define the Weyl modules in the spirit of Chari-Pressley and prove that these Weyl modules are always finite-dimensional and non-zero. In consequence, we obtain a highest weight classification of finite-dimensional simple representations when M = N . Some concrete simple representations are constructed via evaluation morphisms.

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Introduction to Quantum Groups

Cited by 992 publications

References 0 publications

A diagrammatic approach to categorification of quantum groups I

A diagrammatic approach to categorification of quantum groups I

Differential graded categories

Representations of quantum affine superalgebras

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