Tilting modules for the current algebra of a simple Lie algebra

Details Tilting modules for the current algebra of a simple Lie algebra Tilting modules for the current algebra of a simple Lie algebra

2012-02-27

arxiv.org/abs/1202.6050v1

Mathematics

Representation Theory

Scientific paper

The category of level zero representations of current and affine Lie algebras shares many of the properties of other well-known categories which appear in Lie theory and in algebraic groups in characteristic p and in this paper we explore further similarities. The role of the standard and co-standard module is played by the finite-dimensional local Weyl module and the dual of the infinite-dimensional global Weyl module respectively. We define the canonical filtration of a graded module for the current algebra. In the case when $\lie g$ is of type $\lie{sl}_{n+1}$ we show that the well-known necessary and sufficient homological condition for a canonical filtration to be a good (or a $\nabla$-filtration) also holds in our situation. Finally, we construct the indecomposable tilting modules in our category and show that any tilting module is isomorphic to a direct sum of indecomposable tilting modules.

Affiliated with

Also associated with

No associations

Rating

Tilting modules for the current algebra of a simple Lie algebra 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 Tilting modules for the current algebra of a simple Lie algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tilting modules for the current algebra of a simple Lie algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-605053