Standard monomial bases and geometric consequences for certain rings of invariants

2005/06/05 by V. Lakshmibai, Lakshmibai, V., P. Shukla +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #math.AC #math.AG #msc:17B05 #msc:17B10

paper · pdf · doi:10.48550/arxiv.math/0506088

35 pages

arxiv created 2005/06/05 · arxiv updated 2009/12/01

Abstract

Consider the diagonal action of SL_n(K) on the affine space X=V^{⊕ m}⊕ (V^*)^{⊕ q} where V=Kⁿ, 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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