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Standard monomial bases and geometric consequences for certain rings of invariants

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Abstract

Consider the diagonal action ofSL n (K) on the affine spaceX = V⊕m ⊕ (V*)⊕q whereV = K n,K an algebraically closed field of arbitrary characteristic andm,q > n. We construct a ‘standard monomial’’ basis for the ring of invariantsK[X]SL n (K). As a consequence, we deduce thatK[X]SL n (K) is Cohen-Macaulay. We also present the first and second fundamental theorems forSL n (K)- actions.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, 02115, Boston, MA, USA

    V. Lakshmibai

  2. Department of Mathematics, Suffolk University, 02114, Boston, MA, USA

    P. Shukla

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  1. V. Lakshmibai
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  2. P. Shukla
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Correspondence to V. Lakshmibai.

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Lakshmibai, V., Shukla, P. Standard monomial bases and geometric consequences for certain rings of invariants. Proc. Indian Acad. Sci. (Math. Sci.) 116, 9–36 (2006). https://doi.org/10.1007/BF02829736

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  • DOI: https://doi.org/10.1007/BF02829736

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