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# The invariant theory of matrices

Author: Corrado De Concini; Claudio Procesi Providence : American Mathematical Society, 2017. ©2017 University Lecture Series. eBook : Document : EnglishView all editions and formats 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.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic booksElectronic book Print version:De Concini, Corrado.Invariant theory of matrices.Providence, Rhode Island : American Mathematical Society, [2017](DLC) 2017041943(OCoLC)1005832940 Document, Internet resource Internet Resource, Computer File Corrado De Concini; Claudio Procesi Find more information about: Corrado De Concini Claudio Procesi 9781470443467 1470443465 1017004736 1 online resource (151 pages) : illustrations. Introduction -- Preliminaries -- Representation theory -- Algebras with trace -- Modules -- Good filtrations and quasi-hereditary algebras -- The Schur algebra -- Double tableaux -- Modules for the Schur algebra -- Rational GL(m)-modules -- Tensor products -- A reduction for invariants of several matrices -- Polarization and specialization -- Exterior products -- Matrix functions and invariants -- Relations -- Describing Km -- Km versus K̃m -- Preliminary facts -- The Schur algebra of the free algebra. University Lecture Series. Corrado De Concini, Claudio Procesi.

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Provides 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  Read more...

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