University of Illinois Urbana-Champaign

The Grothendieck-Cousin complex on G/B x G/B

LaFramboise, Thomas Louis

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Description

Title
The Grothendieck-Cousin complex on G/B x G/B
Author(s)
LaFramboise, Thomas Louis
Issue Date
1995
Doctoral Committee Chair(s)
Ullom, Stephen V.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
  • In his 1978 paper, The Grothendieck-Cousin complex of an induced representation, G. Kempf computes the Cousin complex corresponding to an induced representation of a reductive algebraic group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.
  • Instead of considering G/B, we analyze the analagous situation for $G/B\times G/B$. The Cousin complex corresponding to an induced representation in this case consists of G-modules. We are able to study the terms of the complex by exploiting parallels between the B-action on G/B and the G-action on $G/B\times G/B$--there is a natural one-to-one correspondence between the orbits of these actions. Our work here is greatly simplified by reducing to the affine situation and applying the theory of A-G modules. We construct a spectral sequence relating the terms of the complexes. Finally, an application to the theory of D-modules is given.
Type of Resource
text
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http://hdl.handle.net/2142/19729
Copyright and License Information
Copyright 1995 LaFramboise, Thomas Louis

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