(q,t)-analogues and GLn(Fq)

Victor Reiner, Dennis Stanton

Research output: Contribution to journalArticle

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Abstract

We start with a (q,t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q,t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict tableaux and Macdonald's "7 th variation" of Schur functions, the other relating to permutation statistics and Hilbert series from the invariant theory of GLn(Fq) .

Original languageEnglish (US)
Pages (from-to)411-454
Number of pages44
JournalJournal of Algebraic Combinatorics
Volume31
Issue number3
DOIs
StatePublished - May 1 2010

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Keywords

  • Coxeter complex
  • Finite field
  • Gaussian coefficient
  • Invariant theory
  • Principal specialization
  • Steinberg character
  • Tits building
  • q-binomial
  • q-multinomial

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