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The geometry of generalized Steinberg varieties

The geometry of generalized Steinberg varieties
The geometry of generalized Steinberg varieties
For a reductive, algebraic group, G, the Steinberg variety of G is the set of all triples consisting of a unipotent element, u, in G and two Borel subgroups of G that contain u. We define generalized Steinberg varieties that depend on four parameters and analyze in detail two special cases that turn out to be related to distinguished double coset representatives in the Weyl group. Using one of the two special cases, we define a parabolic version of a map from the Weyl group to a set of nilpotent orbits of G in Lie(G) defined by Joseph and study some of its properties.
steinberg variety, springer representations
0001-8708
396-416
Douglass, J. Matthew
d4e6884d-db5f-4e33-9479-42bacaae5270
Roehrle, Gerhard
85f9d4eb-d522-4a95-bde9-300e8e3e7886
Douglass, J. Matthew
d4e6884d-db5f-4e33-9479-42bacaae5270
Roehrle, Gerhard
85f9d4eb-d522-4a95-bde9-300e8e3e7886

Douglass, J. Matthew and Roehrle, Gerhard (2004) The geometry of generalized Steinberg varieties. Advances in Mathematics, 187 (2), 396-416. (doi:10.1016/j.aim.2003.09.002).

Record type: Article

Abstract

For a reductive, algebraic group, G, the Steinberg variety of G is the set of all triples consisting of a unipotent element, u, in G and two Borel subgroups of G that contain u. We define generalized Steinberg varieties that depend on four parameters and analyze in detail two special cases that turn out to be related to distinguished double coset representatives in the Weyl group. Using one of the two special cases, we define a parabolic version of a map from the Weyl group to a set of nilpotent orbits of G in Lie(G) defined by Joseph and study some of its properties.

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More information

Submitted date: January 2003
Published date: October 2004
Keywords: steinberg variety, springer representations

Identifiers

Local EPrints ID: 38463
URI: http://eprints.soton.ac.uk/id/eprint/38463
ISSN: 0001-8708
PURE UUID: c2a28b78-8705-4648-905b-d82b8a5b1dad

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Date deposited: 09 Jun 2006
Last modified: 15 Jul 2019 19:02

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