Standard monomial bases and geometric consequences for certain rings of invariants

V. Lakshmibai; P. Shukla

Standard monomial bases and geometric consequences for certain rings of invariants

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

Authors: V. Lakshmibai , P. Shukla

Abstract

Consider the diagonal action of $SL_n(K)$ on the affine space $X=V^{\oplus m}\oplus (V^*)^{\oplus q}$ where $V=K^n, K$ an algebraically closed field of arbitrary characteristic and $m,q>n$ . We construct a "standard monomial" basis for the ring of invariants $K[X]^{SL_n(K)}$ . As a consequence, we deduce that $K[X]^{SL_n(K)}$ is Cohen-Macaulay. We also present the first and second fundamental theorems for $SL_n(K)$ -actions.

Keywords

standard monomial basis ring of invariants sl_n cohen-macaulay fundamental theorems

Cite

@article{arxiv.math/0506088,
  title  = {Standard monomial bases and geometric consequences for certain rings of invariants},
  author = {V. Lakshmibai and P. Shukla},
  journal= {arXiv preprint arXiv:math/0506088},
  year   = {2007}
}

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35 pages

Standard monomial bases and geometric consequences for certain rings of invariants

Abstract

Keywords

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