The invariant theory of matrices
Author(s)
Bibliographic Information
The invariant theory of matrices
（University lecture series, v. 69）
American Mathematical Society, c2017
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 145-148) and indexes
Description and Table of Contents
Description
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of $m\times m$ matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation.
Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
Table of Contents
Introduction and preliminaries
The classical theory
Quasi-hereditary algebras
The Schur algebra
Matrix functions and invariants
Relations
The Schur algebra of a free algebra
Bibliography
General index
Symbol index.
by "Nielsen BookData"
