Difference equations and symmetric polynomials defined by their zeros
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 1/2, 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.
 Publication:

eprint arXiv:qalg/9610017
 Pub Date:
 October 1996
 DOI:
 10.48550/arXiv.qalg/9610017
 arXiv:
 arXiv:qalg/9610017
 Bibcode:
 1996q.alg....10017K
 Keywords:

 Mathematics  Quantum Algebra;
 05Exx;
 33xx
 EPrint:
 Preprint March 1996, 14 pages, Plain TeX