Standard monomial bases and geometric consequences for certain rings of invariants

Details Standard monomial bases and geometric consequences for certain rings of invariants Standard monomial bases and geometric consequences for certain rings of invariants

2005-06-05

arxiv.org/abs/math/0506088v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

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.

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