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Young diagrammatic methods in non-commutative invariant theory

  • Yasuo Teranishi (a1)
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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⊕S 2(V)⊕…, and

K′V› = K⊕V⊕⊕2(V)⊕⊕3 V⊕&

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.

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Copyright
COPYRIGHT: © Editorial Board of Nagoya Mathematical Journal 1991
References
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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