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Young diagrammatic methods in non-commutative invariant theory

Published online by Cambridge University Press:  22 January 2016

Yasuo Teranishi
Yasuo Teranishi*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
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In this paper we will study some aspects of non-commutative invariant theory. Let V be a finite-dimensional vector space over a field K of characteristic zero and let

K[V] = K⊕V⊕S2(V)⊕…, and

K′V› = K⊕V⊕⊕2(V)⊕⊕3V⊕&

be respectively the symmetric algebra and the tensor algebra over V. Let G be a subgroup of GL(V). Then G acts on K[V] and K′V›. Much of this paper is devoted to the study of the (non-commutative) invariant ring K′V›G of G acting on K′V›.

In the first part of this paper, we shall study the invariant ring in the following situation.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991 , pp. 15 - 34
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

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