Interpolation analogues of Schur Q-functions

2003/05/29 by Vladimir Ivanov, Vladimir N. Ivanov, Ivanov, Vladimir N. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.CO #math.RT #msc:05C38 #msc:05E05 #msc:05E10 #msc:20C25 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0305419

LaTeX2e, 20 pages

arxiv created 2003/05/29 · arxiv updated 2009/11/30

Abstract

We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula for the transition coefficients between multiparameter Schur Q-functions with different parameters. We write an explicit Pfaffian expression for the dimension of skew shifted Young diagram. This paper is a continuation of author's paper math.CO/0303169 and is a partial projective analogue of the paper by A. Okounkov and G. Olshanski q-alg/9605042, and of the paper by G. Olshanski, A. Regev and A. Vershik math.CO/0110077.

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