Standard monomials for partitions

G. Hegedus, L. Rónyai

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let F be a field, and α 0,...,α k-1 be k distinct elements of F. Let λ =(λ 1,..., λ k) be a partition of n and V λ be the set of all vectors v=(v 1,...,v n) F n such that|{j ∈[n] : v ji}|=λ i+1 for 0≦ i ≦ k-1. We describe the lexicographic standard monomials of the ideal of polynomials from F[x 1,...,x n] which vanish on the set V λ. In the proof we give a new description of the orthogonal complement (S λ)) (with respect to the James scalar product) of the Specht module S λ. As applications, a basis of (S λ) is exhibited, and we obtain a combinatorial description of the Hilbert function of V λ... Our approach gives also the deglex standard monomials of V λ, and hence provides a new proof of a result of A. M. Garsia and C. Procesi [10].

Original languageEnglish
Pages (from-to)193-212
Number of pages20
JournalActa Mathematica Hungarica
Volume111
Issue number3
DOIs
Publication statusPublished - May 1 2006

Keywords

  • Gröbner basis
  • Hilbert function
  • Specht module
  • Standard monomial
  • Tableau

ASJC Scopus subject areas

  • Mathematics(all)

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