Generalized Weyl modules and Demazure submodules of level-zero extremal weight modules

2017/01/29 by Nomoto, Fumihiko
#81R10 #81R50 #FOS: Mathematics #Primary 17B37 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 33D52

paper · doi:10.48550/arxiv.1701.08377

Abstract

We study a relationship between the graded characters of generalized Weyl modules W_{w λ}, w ∈ W, over the positive part of the affine Lie algebra and those of specific quotients V_w^- (λ) / X_w^- (λ), w ∈ W, of the Demazure submodules V_w^- (λ) of the extremal weight modules V(λ) over the quantum affine algebra, where W is the finite Weyl group and λ is a dominant weight. More precisely, we prove that a specific quotient of the Demazure submodule is a quantum analog of a generalized Weyl module.

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