Filtrations in Modular Representations of Reductive Lie Algebras

Details Filtrations in Modular Representations of Reductive Lie Algebras Filtrations in Modular Representations of Reductive Lie Algebras

2007-03-18

arxiv.org/abs/math/0703528v2

Mathematics

Representation Theory

The current version of this paper will appear in Algebra Colloquium

Scientific paper

Let $G$ be a connected reductive algebraic group $G$ over an algebraically closed field $k$ of prime characteristic $p$, and $\ggg=\Lie(G)$. In this paper, we study modular representations of the reductive Lie algebra $\ggg$ with $p$-character $\chi$ of standard Levi-form associated with an index subset $I$ of simple roots. With aid of support variety theory we prove a theorem that a $U_\chi(\ggg)$-module is projective if and only if it is a strong "tilting" module, i.e. admitting both $\cz_Q$- and $\cz^{w^I}_Q$-filtrations (to see Theorem \ref{THMFORINV}). Then by analogy of the arguments in \cite{AK} for $G_1T$-modules, we construct so-called Andersen-Kaneda filtrations associated with each projective $\ggg$-module of $p$-character $\chi$, and finally obtain sum formulas from those filtrations.

Affiliated with

Also associated with

No associations

Rating

Filtrations in Modular Representations of Reductive Lie 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 Filtrations in Modular Representations of Reductive Lie Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Filtrations in Modular Representations of Reductive Lie Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31659