Representation Theory

Author(s): Jonathan Kujawa
Journal: Represent. Theory 10 (2006), 49-85.
MSC (2000): Primary 20C20, 05E99; Secondary 17B10
Posted: February 16, 2006
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Abstract: This paper provides results on the modular representation theory of the supergroup $GL(m\vert n).$ 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 $GL(m\vert n)$ has non-conjugate Borel subgroups and we show how Serganova's odd reflections give rise to canonical crystal isomorphisms.

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Jonathan Kujawa
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: kujawa@math.uga.edu

DOI: 10.1090/S1088-4165-06-00219-6
PII: S 1088-4165(06)00219-6
Received by editor(s): November 17, 2003
Received by editor(s) in revised form: January 3, 2006
Posted: February 16, 2006
Additional Notes: Research was supported in part by NSF grant DMS-0402916
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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