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

DOI:
https://doi.org/10.1090/S0002-9939-02-06716-3

Published electronically:
October 1, 2002

MathSciNet review:
1955270

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial with . 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 associated with the nonsymmetric Jack polynomials for .

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Additional Information

**Dan Marshall**

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

Email:
Dan.Marshall@anu.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-02-06716-3

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