Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions

Fourier, G. and Littelmann, P. (2007) Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions. Advances in Mathematics, 211(2), pp. 566-593. (doi: 10.1016/j.aim.2006.09.002)

Abstract

<p>We study finite-dimensional representations of current algebras, loop algebras and their quantized versions. For the current algebra of a simple Lie algebra of type ADE, we show that Kirillov–Reshetikhin modules and Weyl modules are in fact all Demazure modules. As a consequence one obtains an elementary proof of the dimension formula for Weyl modules for the current and the loop algebra. Further, we show that the crystals of the Weyl and the Demazure module are the same up to some additional label zero arrows for the Weyl module.</p> <p>For the current algebra Cg of an arbitrary simple Lie algebra, the fusion product of Demazure modules of the same level turns out to be again a Demazure module. As an application we construct the Cg-module structure of the Kac–Moody algebra -module V(ℓΛ_0) as a semi-infinite fusion product of finite-dimensional Cg-modules.</p>

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Fourier, G., and Littelmann, P.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• ISSN: 0001-8708
• ISSN (Online): 1090-2082
• Copyright Holders: Copyright © 2006 Elsevier Inc.
• First Published: First published in Advances in Mathematics 211(2):566-593
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher