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Factorization Properties of the q-Specialization of Schubert Polynomials
Vincent Prosper
Gaspard Monge Institute, University of Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2, France
Annals of Combinatorics 4 (1) p.91-107 March, 2000
AMS Subject Classification:05E10, 14M15
Abstract:
Schubert polynomials are a linear basis of the ring of polynomials in x = {x1,...,xn} with coefficients in a second set of variables y = {y1, y2, ...}. Two specializations of y are classical: y = {0, 1, 2, ...} or {1, q, q2, ...}, and contain as subfamilies factorial and q-factorial Schur functions. We give here a factorization property when one specializes both x and y into successive powers of q. It involves describing the specialization to x = 1, q, q2, ..., y = 0, which we study through a generating function. The whole description is given by introducing a double statistics on tableaux.
Keywords: Schubert polynomials, factorial and q-factorial Schur functions

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