Kelly, John Columba (1975) The fields generated by the values of the characters of the finite classical groups. PhD thesis, University of Warwick.

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Abstract

The absolutely irreducible characters of a finite group G take their values in a cyclotomic extension of the field of rational numbers, and so are defined in some cyclotomic extension L of any field K of characteristic zero. The purpose of this thesis is to determine the smallest such extension L where K is either the rational field or a certain p-adic field, and G is one of the classical groups defined over a finite field with q elements, Fq. In particular it is shown that there is at least one group defined over Fq in each classical "family" whose characters take values in the ring of Witt vectors W(Fq).

Section 5 of the thesis deals with a different problem. A theorem of Frobenius, expressing all the irreducible characters of the symmetric groups as integral linear combinations of the characters of certain permutation representations, is generalised to the Weyl group W(Cn), and some consequences for the representation theory of finite groups with (B,N)-pairs are deduced.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Group theory, Finite groups, Finite fields (Algebra)
Official Date:	September 1975
Dates:	Date Event September 1975 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Lusztig, George
Sponsors:	Science Research Council (Great Britain)
Extent:	115 leaves
Language:	eng

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