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Applications of representation theory

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Alghofari, AR (1998) Applications of representation theory. Coursework Master thesis, University of Tasmania.

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Abstract

This thesis presents two applications of representation theory of locally compact
groups. The first is concerned with random walks, the second with Mackey's
Intertwining Number Theorem.
Firstly, we consider the random walk on a collection of chambers bounded
by hyperplanes in a given subspace E of Rn+1 . Initially, a particular transition
probability is used in the first part of this analysis, and the identification of
the collection of chambers with a reflection group provides necessary tools for
obtaining a criterion for the recurrence of that walk. Next, the techniques of
representation theory are used to deal with the generalization of the random walk
when transition probability is considered to be a general probability measure on
the group concerned.
Secondly, Mackey's Intertwining Number Theorem for one dimensional representations
of open and closed subgroups of a given locally compact group G
is generalized. A similar result to Mackey's is obtained in the case where the
representations are finite dimensional. The recent developments in the theory of
Aqp, spaces (in which such spaces are recognized as preduals of spaces of intertwining
operators of induced representations) are being simplified under the condition
that the subgroups are open and closed. These results, together with the fact that
the space of intertwining operators between two representations can be identified
with the dual of the G-tensor product of the corresponding representation spaces
(endowed with the greatest cross-norm) are used to carry out the analysis.

Item Type: Thesis (Coursework Master)
Keywords: Representations of groups, Representations of algebras, Random walks (Mathematics)
Copyright Holders: The Author
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Copyright 1998 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
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Additional Information:

Thesis (M.Sc.)--University of Tasmania, 1998. Includes bibliographical references

Date Deposited: 25 Nov 2014 00:48
Last Modified: 23 Aug 2017 05:18
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