The three topics discussed in the three chapters of this thesis are
only loosely related. Strictly speaking, only Chapter 1 is about
invariant theory. Namely, it is shown that the invariant theory of
the orthogonal group acting on the direct sum of several copies of
the standard vector representation differs drastically over fields
of characteristic 2 from the well-known theory in all other
characteristics. As a result, we encounter non-classical behaviour
also over the ring of integers. In Chapter 2, we work over the
field of complex numbers. We obtain new formulae for the
irreducible characters of the classical matrix groups, more
specifically, we express them as fractions of polynomials in the
entries of matrix powers. Our formulae can be viewed as unexpected
constructions of conjugation invariant functions of matrices. In
Chapter 3, we work over the real field, and we prove inequalities
for positive semi-definite matrices. Chapter 3 is the most
down-to-earth part of this thesis, it ends with an application to
the problem of bounding from below the norm of a product of linear
functionals.
General
Imprint: |
Lap Lambert Academic Publishing
|
Country of origin: |
Germany |
Release date: |
December 2010 |
First published: |
December 2010 |
Authors: |
Peter Frenkel
|
Dimensions: |
229 x 152 x 4mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
68 |
ISBN-13: |
978-3-8433-8302-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
LSN: |
3-8433-8302-2 |
Barcode: |
9783843383028 |
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