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Interpolation Analogs of Schur Q-Functions

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Abstract

We introduce interpolation analogs of the Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-row functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a quotient 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 a skew shifted Young diagram. This paper is a continuation of the author's paper math. CO/0303169 and a partial projective analog of the paper q-alg/9605042 by A. Okounkov and G. Olshanski and the paper math. CO/0110077 by G. Olshanski, A. Regev, and A. Vershik. Bibliography: 36 titles.

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  1. Independent University of Moscow, Russia

    V. N. Ivanov

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  1. V. N. Ivanov
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 307, 2004, pp. 99–119.

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Ivanov, V.N. Interpolation Analogs of Schur Q-Functions. J Math Sci 131, 5495–5507 (2005). https://doi.org/10.1007/s10958-005-0422-6

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  • DOI: https://doi.org/10.1007/s10958-005-0422-6

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