The product of a nonsymmetric Jack polynomial with a linear function
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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 $|\eta |=|\nu | + 1$.References
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Additional Information
- Dan Marshall
- Affiliation: School of Humanities, Australian National University, Canberra, 0200, Australia
- Email: Dan.Marshall@anu.edu.au
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1817-1827
- MSC (2000): Primary 33C45; Secondary 05A10
- DOI: https://doi.org/10.1090/S0002-9939-02-06716-3
- MathSciNet review: 1955270