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Title:The Grothendieck-Cousin complex on G/B x G/B
Author(s):LaFramboise, Thomas Louis
Doctoral Committee Chair(s):Ullom, Stephen V.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:1995
Type:Text
Language:English
URI:http://hdl.handle.net/2142/19729
Rights Information:Copyright 1995 LaFramboise, Thomas Louis
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9624402
OCLC Identifier:(UMI)AAI9624402


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