2004/04/05 by M. Kasatani, Kasatani, M., T. Miwa +6
Mathematics · Physics and Astronomy · #05E05 #33D52 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E05 #msc:33D52
paper · pdf · doi:10.48550/arxiv.math/0404079
19 pages, Proceedings of "Jack and Macdonald polynomials" meeting (ICMS, Edinburgh, September 2003)
arxiv created 2004/04/05 · openalex publication_date 2004/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 α= -2. As a corollary we present an explicit formula for the Hilbert-Poincarè 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 t2 q = 1 is also presented. We also give similar results for the interpolation Jack polynomials.