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The product of a nonsymmetric Jack polynomial with a linear function

Author: Dan Marshall
Journal: Proc. Amer. Math. Soc. 131 (2003), 1817-1827
MSC (2000): Primary 33C45; Secondary 05A10
Published electronically: October 1, 2002
MathSciNet review: 1955270
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Abstract: In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial $E_{\eta}(z)$ with $z_i$. This decomposition generalises a recurrence formula satisfied by single variable orthogonal polynomials on the unit circle. The decomposition also allows the evaluation of the generalised binomial coefficients $\binom{\eta}{\nu}$ associated with the nonsymmetric Jack polynomials for $\vert\eta\vert=\vert\nu\vert + 1$.

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Additional Information

Dan Marshall
Affiliation: School of Humanities, Australian National University, Canberra, 0200, Australia

Keywords: Jack polynomials, Pieri formula, generalized binomial coefficients
Received by editor(s): May 14, 2001
Received by editor(s) in revised form: December 7, 2001, January 11, 2002, and January 22, 2002
Published electronically: October 1, 2002
Additional Notes: The author thanks Peter Forrester for useful discussions and for bringing to his attention the paper by Knop and Sahi, and an anonymous referee for helpful comments. This work was supported by an Australian Postgraduate Award.
Communicated by: John R. Stembridge
Article copyright: © Copyright 2002 American Mathematical Society