Coincident root loci and Jack and Macdonald polynomials for special values of the parameters
Abstract
We consider the coincident root loci consisting of the polynomials with at least two double roots andpresent a linear basis of the corresponding ideal in the algebra of symmetric polynomials in terms of the Jack polynomials with special value of parameter $\alpha = 2.$ As a corollary we present an explicit formula for the HilbertPoincarè series of this ideal and the generator of the minimal degree as a special Jack polynomial. A generalization to the case of the symmetric polynomials vanishing on the double shifted diagonals and the Macdonald polynomials specialized at $t^2 q = 1$ is also presented. We also give similar results for the interpolation Jack polynomials.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 DOI:
 10.48550/arXiv.math/0404079
 arXiv:
 arXiv:math/0404079
 Bibcode:
 2004math......4079K
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Combinatorics;
 33D52;
 05E05
 EPrint:
 19 pages, Proceedings of "Jack and Macdonald polynomials" meeting (ICMS, Edinburgh, September 2003)