Finite-Dimensional Representations of Hyper Loop Algebras

Details Finite-Dimensional Representations of Hyper Loop Algebras Finite-Dimensional Representations of Hyper Loop Algebras

2006-12-07

arxiv.org/abs/math/0612174v3

Pacific J. Math. 233 (2007), 371--402

Mathematics

Representation Theory

Final version to appear in the Pacific Journal of Mathematics, 24 pages

Scientific paper

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg's Tensor Product Theorem, and the construction of positive characteristic analogues of the Weyl modules as defined by Chari and Pressley in the characteristic zero setting. Furthermore, we start the study of reduction modulo p and prove that every irreducible module of a hyper loop algebra can be constructed as a quotient of a module obtained by a certain reduction modulo p process applied to a suitable characteristic zero module. We conjecture that the Weyl modules are also obtained by reduction modulo p. The conjecture implies a tensor product decomposition for the Weyl modules which we use to describe the blocks of the underlying abelian category.

Affiliated with

Also associated with

No associations

Rating

Finite-Dimensional Representations of Hyper Loop Algebras 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 Finite-Dimensional Representations of Hyper Loop Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-Dimensional Representations of Hyper Loop Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-16294