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

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      https://www.ias.ac.in/article/fulltext/pmsc/116/01/0009-0036

    • Keywords

       

      Invariants; determinantal varieties; standard monomials

    • Abstract

       

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

    • Author Affiliations

       

      V Lakshmibai1 P Shukla2

      1. Department of Mathematics, Northeastern University, Boston, MA - 02115, USA
      2. Department of Mathematics, Suffolk University, Boston, MA - 02114, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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