First Fundamental Theorem of Invariant Theory for covariants of classical groups

D. A. Shmel'kin

First Fundamental Theorem of Invariant Theory for covariants of classical groups

Algebraic Geometry 2007-05-23 v1 Rings and Algebras Representation Theory

Authors: D. A. Shmel'kin

Abstract

Let $U(G)$ be a maximal unipotent subgroup of one of classical groups $G=GL(V),O(V),Sp(V)$ . Let $W$ be a direct sum of copies of $V$ and its dual $V*$ . For the natural action $U(G):W$ , we describe a minimal system of homogeneous generators for the algebra of $U(G)$ -invariant regular functions on $W$ . For $G=GL(V)$ , we also describe the syzygies among these generators in some particular cases.

Keywords

invariant theory classical groups maximal unipotent subgroup covariants homogeneous generators syzygies

Cite

@article{arxiv.math/0006110,
  title  = {First Fundamental Theorem of Invariant Theory for covariants of classical groups},
  author = {D. A. Shmel'kin},
  journal= {arXiv preprint arXiv:math/0006110},
  year   = {2007}
}

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13 pages, LaTeX 2.09

First Fundamental Theorem of Invariant Theory for covariants of classical groups

Abstract

Keywords

Cite

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