Difference equations and symmetric polynomials defined by their zeros

Knop F, Sahi S (1996)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1996

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Publisher: Oxford University Press (OUP): Policy H - Oxford Open Option A

Journal Issue: 10

DOI: 10.1155/S1073792896000311

Abstract

In this paper, we introduce a new family of symmetric polynomials which depends on a parameter r. They are defined by specifying certain of their zeros. For the parameter values ½, 1, and 2 they have an interpretation in terms of Capelli identities.

First, we give explicit formulas in some special cases. Then we show that the polynomials can also be defined in terms of difference equations. As a corollary we obtain that their top homogeneous part is a Jack polynomial. This is used to give a new proof of the Pieri formula for Jack polynomials.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F., & Sahi, S. (1996). Difference equations and symmetric polynomials defined by their zeros. International Mathematics Research Notices, 10. https://dx.doi.org/10.1155/S1073792896000311

MLA:

Knop, Friedrich, and Siddhartha Sahi. "Difference equations and symmetric polynomials defined by their zeros." International Mathematics Research Notices 10 (1996).

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