Starkey, Andrew John (1975) Characters of the generic Hecke algebra of a system of bn-pairs. PhD thesis, University of Warwick.

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Abstract

This thesis is concerned vith the construction of the
characters of the generic Hecke algebra of a system of BN-
pairs of type (W,R). The approach used exploits the connection
between these characters and those of the Coxeter group W.
Part I of the thesis gives definitions, results and
conjectures relevant to calculating the characters of any
generic Hecke algebra and Part II applies these results to
the problem of calculating the characters of certain generic
Hecke algebras.
In more detail: Chapter 1 gives basic definitions
and describes the connection between the characters of the
generic Hecke algebra and those of the Coxeter group W.
Chapter 2 divides the problem of calculating the
characters into two parts and gives conjectures and results
concerning one of these 'parts'. The results given solve
this part of the 'problem ( in a non-explicit manner) for
some but not all generic Hecke algebras.
The last three chapters are all concerned with solving
the other 'part' of the problem by an inductive method which
uses the connection described in chapter 1.
Chapter 3 describes this method ( the 'circle product').
Chapters 4 and 5 apply this method to a particular 'family'
of generic Hecke algebras, culminating in an explicit formula
(given in theorem 5.3.9) for certain character values.
The appendices contain tables of character values of
some generic Hecke algebras.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebra
Official Date:	July 1975
Dates:	Date Event July 1975 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Green, J. A. (James Alexander)
Extent:	iii, 98 leaves : illustrations
Language:	eng

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