A method to derive explicit formulas for an elliptic generalization of the Jack polynomials
2006 (English)In: Jack, Hall-Littlewood and Macdonald Polynomials / [ed] Kuznetsov, VB; Sahi, S, PROVIDENCE, RI: AMER MATHEMATICAL SOC , 2006, Vol. 417, 257-270 p.Conference paper (Refereed)
We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case.
Place, publisher, year, edition, pages
PROVIDENCE, RI: AMER MATHEMATICAL SOC , 2006. Vol. 417, 257-270 p.
, CONTEMPORARY MATHEMATICS SERIES, ISSN 0271-4132 ; 417
quantum integrable systems, symmetric polynomials
IdentifiersURN: urn:nbn:se:kth:diva-42105ISI: 000243404400015ISBN: 0-8218-3683-8OAI: oai:DiVA.org:kth-42105DiVA: diva2:446230
Workshop on Jack, Hall-Littlewood and Macdonald Polynomials. ICMS, Edinburgh, SCOTLAND. SEP 23-26, 2003
QC 201110062011-10-062011-10-052011-10-06Bibliographically approved