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New Constructions in Classical Invariant Theory


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  • Product 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.

Product Specifications
SKU :COC32847
AuthorPeter Frenkel
Number of Pages68
Publishing Year12/17/2010
Edition1 st
Book TypeAlgebra
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-29 00:00:00
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