Crystal structures arising from representations of $GL(m|n)$
| dc.creator | Kujawa, Jonathan | |
| dc.date | 2003-11-14 | |
| dc.date | 2003-11-21 | |
| dc.date.accessioned | 2026-07-07T05:02:55Z | |
| dc.date.available | 2026-07-07T05:02:55Z | |
| dc.description | 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. | |
| dc.description | 36 Pages, reference added | |
| dc.identifier | https://arxiv.org/abs/math/0311251 | |
| dc.identifier | http://arxiv.org/abs/math/0311251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69205 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C20, 05E99, 17B10 | |
| dc.title | Crystal structures arising from representations of $GL(m|n)$ | |
| dc.type | text |