Fusion product structure of Demazure modules
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Publication:2348546
DOI10.1007/S10468-014-9495-6zbMATH Open1320.17013arXiv1311.2224OpenAlexW1968731439MaRDI QIDQ2348546
Author name not available (Why is that?)
Publication date: 15 June 2015
Published in: (Search for Journal in Brave)
Abstract: Let g be a finite-dimensional complex simple Lie algebra. Fix a non-negative integer l, we consider the set of dominant weights {lambda} of g such that l{Lambda}_0+{lambda} is a dominant weight for the corresponding untwisted affine Kac-Moody algebra. For these special family of dominant weights, we show that the fusion product of an irreducible g-module V({lambda}) and a finite number of special family of g-stable Demazure modules of level l (considered in [15] and [16]), for the current algebra g[t] associated to g, again turns out to be a Demazure module. This fact is closely related with several important conjectures. We use this result to construct the g[t]-module structure of the irreducible module V(l{Lambda}_0 + {lambda}) as a semi-infinite fusion product of finite dimensional g[t]-modules as conjectured in [16]. As a second application we give further evidence to the conjecture on the generalization of Schur positivity (see [7]).
Full work available at URL: https://arxiv.org/abs/1311.2224
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