(q,t)-analogues and GL_n(F_q)

2008/04/18 by Reiner, Victor, Stanton, Dennis
#05A17 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0804.3074

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 ``seventh variation'' of Schur functions, the other relating to permutation statistics and Hilbert series from the invariant theory of GL_n(F_q).

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