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Inhaltsangabe
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.
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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.
Biografía del autor
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.
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New Constructions in Classical Invariant Theory
Verlag:
LAP LAMBERT Academic Publishing, 2010
ISBN 10: 3843383022
ISBN 13: 9783843383028
Neu
Softcover
Anbieter: moluna, Greven, Deutschland
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Zustand: New. Artikel-Nr. 5468150
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New Constructions in Classical Invariant Theory
Verlag:
LAP LAMBERT Academic Publishing Dez 2010, 2010
ISBN 10: 3843383022
ISBN 13: 9783843383028
Neu
Taschenbuch
Anbieter: buchversandmimpf2000, Emtmannsberg, BAYE, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: Neu. Neuware -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.Books on Demand GmbH, Überseering 33, 22297 Hamburg 68 pp. Englisch. Artikel-Nr. 9783843383028
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