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

Details Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions

2005-09-13

arxiv.org/abs/math/0509276v4

Mathematics

Representation Theory

Scientific paper

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 {\tt 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. For the current algebra $\Lgc$ 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 $\Lgc$-module structure of the Kac-Moody algebra $\Lhg$-module $V(\ell\Lam_0)$ as a semi-infinite fusion product of finite dimensional $\Lgc$--modules.

Affiliated with

Also associated with

No associations

Rating

Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-703832