Deriziotis, D. I. (1977) The Brauer complex and its applications to the Chevalley groups. PhD thesis, University of Warwick.

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Abstract

This thesis, is concerned with the determination of the connected centralizers of semi-simple elements in a Chevalley group. To deal with this problem we shall use the recent work of R. Carter [6] and a new tool for the study of algebraic groups - the so called Brauer complex. This complex has been first defined by J. Humphreys [11] in the context of the modular representation theory of the finite Chevalley groups of universal type. Now, in our version, the Brauer complex can be also used for the ordinary representation theory of the finite Chevalley groups of adjoint type. For, Deligne and Lusztig in their fundamental work [9] have constructed for these groups certain families of irreducible complex representations whose degrees can be obtained if we know what subgroups of the finite Chevalley groups are the connected centralizers of semi-simple elements.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Brauer groups, Chevalley groups
Official Date:	December 1977
Dates:	Date Event December 1977 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Carter, Roger W. (Roger William)
Extent:	v, 131 leaves
Language:	eng

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