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

dc.creatorKujawa, Jonathan
dc.date2003-11-14
dc.date2003-11-21
dc.date.accessioned2026-07-07T05:02:55Z
dc.date.available2026-07-07T05:02:55Z
dc.descriptionThis 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.description36 Pages, reference added
dc.identifierhttps://arxiv.org/abs/math/0311251
dc.identifierhttp://arxiv.org/abs/math/0311251
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69205
dc.subjectRepresentation Theory
dc.subject20C20, 05E99, 17B10
dc.titleCrystal structures arising from representations of $GL(m|n)$
dc.typetext

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