
New Constructions in Classical Invariant Theory
Juggling with Multilinear Polynomials
Peter Frenkel(Author)
LAP Lambert Academic Publishing
Published on 17. December 2010
Book
Paperback/Softback
68 pages
978-3-8433-8302-8 (ISBN)
Description
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.
More details
Language
English
Place of publication
Germany
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 220 mm
Width: 150 mm
Thickness: 5 mm
Weight
119 gr
ISBN-13
978-3-8433-8302-8 (9783843383028)
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Schweitzer Classification
Person
Péter E. Frenkel, PhD: Studied Mathematics at Eötvös University, Budapest and the Budapest University of Technology and Economics. Worked as Junior Researcher at the Rényi Institute of the Hungarian Academy of Sciences. Postdoctoral Assistant at the University of Geneva, Switzerland.