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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On restrictions of modular spin representations of symmetric and alternating groups


Authors: Alexander S. Kleshchev and Pham Huu Tiep
Journal: Trans. Amer. Math. Soc. 356 (2004), 1971-1999
MSC (2000): Primary 20C20, 20C30, 20C25; Secondary 20B35, 20B20
Published electronically: October 28, 2003
MathSciNet review: 2031049
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Abstract: Let $\mathbb F$ be an algebraically closed field of characteristic $p$ and $H$ be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups $G$ of $H$ and $\mathbb F H$-modules $V$ such that the restriction $V{\downarrow}_G$ is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where $H$ is the Schur's double cover $\hat A_n$ or $\hat S_n$.


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Additional Information

Alexander S. Kleshchev
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: klesh@math.uoregon.edu

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: tiep@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03364-6
PII: S 0002-9947(03)03364-6
Keywords: Representation theory, finite groups
Received by editor(s): October 30, 2002
Received by editor(s) in revised form: April 4, 2003
Published electronically: October 28, 2003
Additional Notes: The authors gratefully acknowledge the support of the NSF (grants DMS-0139019 and DMS-0070647)
Article copyright: © Copyright 2003 American Mathematical Society