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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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