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ON THE SUPPORT VARIETIES FOR DEMAZURE MODULES

Part of: Linear algebraic groups and related topics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  19 March 2012

Benjamin F. Jones  and
Daniel K. Nakano
Benjamin F. Jones
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout, Menomonie, WI 54751, USA (email: [email protected])
Daniel K. Nakano*
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The support varieties for the induced modules or Weyl modules for a reductive algebraic group G were computed over the first Frobenius kernel G1 by Nakano, Parshall and Vella. A natural generalization of this computation is the calculation of the support varieties of Demazure modules over the first Frobenius kernel, B1, of the Borel subgroup B. In this paper we initiate the study of such computations. We complete the entire picture for reductive groups with underlying root systems A1 and A2. Moreover, we give complete answers for Demazure modules corresponding to a particular (standard) element in the Weyl group, and provide results relating support varieties between different Demazure modules which depend on the Bruhat order.

Keywords

support varietiescohomologyDemazure modules

MSC classification

Secondary: 17B56: Cohomology of Lie (super)algebras 20G10: Cohomology theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 343 - 363
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

The first-named author was supported in part by NSF VIGRE grant DMS-0738586, and the second-named author was supported in part by NSF VIGRE grant DMS-1002135.

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