Unimodality of Differences of Specialized Schur Functions

V. Reiner, D. Stanton

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The centered difference of principally specialized Schur functions sλ̃(1,q, . . . ,qn) - qnsλ(1, q, . . . ,qn) is shown to be a symmetric, unimodal polynomial in q with non-negative coefficients for certain choices of λ̃, λ, and n, in which λ̃ is always obtained from λ by adding two cells, and n is chosen to be odd or even depending on λ̃, λ. The basic technique is to find an injection of representations for the symplectic or orthogonal Lie algebras, and interpret the above difference as the principal specialization of the formal character of the quotient. As a special case, a difference of q-binomial coefficients is shown to be unimodal.

Original languageEnglish (US)
Pages (from-to)91-107
Number of pages17
JournalJournal of Algebraic Combinatorics
Volume7
Issue number1
DOIs
StatePublished - Jan 1 1998

Keywords

  • Peck
  • Principal specialization
  • Unimodality

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