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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|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
|Rights Information:||Copyright 1995 LaFramboise, Thomas Louis|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9624402|