Crystal structures arising from representations of $GL(m|n)$

Details Crystal structures arising from representations of $GL(m|n)$ Crystal structures arising from representations of $GL(m|n)$

2003-11-14

arxiv.org/abs/math/0311251v2

Mathematics

Representation Theory

36 Pages, reference added

Scientific paper

This paper provides results on the modular representation theory of the supergroup $GL(m|n).$ Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation theory of a modular analogue of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$. In particular, we obtain a linkage principle and describe the effect of certain translation functors on irreducible supermodules. Furthermore, our approach accounts for the fact that $GL(m|n)$ has non-conjugate Borel subgroups and we show how Serganova's odd reflections give rise to canonical crystal isomorphisms.

Affiliated with

Also associated with

No associations

Rating

Crystal structures arising from representations of $GL(m|n)$ 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 Crystal structures arising from representations of $GL(m|n)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Crystal structures arising from representations of $GL(m|n)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586300