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

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- by Jonathan Kujawa PDF
- Represent. Theory
**10**(2006), 49-85 Request permission

## Abstract:

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.## References

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## Additional Information

**Jonathan Kujawa**- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 720815
- Email: kujawa@math.uga.edu
- Received by editor(s): November 17, 2003
- Received by editor(s) in revised form: January 3, 2006
- Published electronically: February 16, 2006
- Additional Notes: Research was supported in part by NSF grant DMS-0402916
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**10**(2006), 49-85 - MSC (2000): Primary 20C20, 05E99; Secondary 17B10
- DOI: https://doi.org/10.1090/S1088-4165-06-00219-6
- MathSciNet review: 2209849