Rigidity of tilting modules

Details Rigidity of tilting modules Rigidity of tilting modules

2009-09-16

arxiv.org/abs/0909.2935v1

Mathematics

Representation Theory

Scientific paper

Let $U_q$ denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that $q$ is a complex root of unity of odd order and that $U_q$ is %the quantum group version obtained via Lusztig's $q$-divided powers construction. We prove that all regular projective (tilting) modules for $U_q$ are rigid, i.e., have identical radical and socle filtrations. Moreover, we obtain the same for a large class of Weyl modules for $U_q$. On the other hand, we give examples of non-rigid indecomposable tilting modules as well as non-rigid Weyl modules. These examples are for type $B_2$ and in this case as well as for type $A_2$ we calculate explicitly the Loewy structure for all regular Weyl modules. We also demonstrate that these results carry over to the modular case when the highest weights in question are in the so-called Jantzen region. At the same time we show by examples that as soon as we leave this region non-rigid tilting modules do occur.

Affiliated with

Also associated with

No associations

Rating

Rigidity of tilting modules 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 Rigidity of tilting modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity of tilting modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582269