Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials
| dc.creator | Feigin, B. | |
| dc.creator | Jimbo, M. | |
| dc.creator | Miwa, T. | |
| dc.creator | Mukhin, E. | |
| dc.date | 2002-09-04 | |
| dc.date.accessioned | 2026-07-07T04:50:36Z | |
| dc.date.available | 2026-07-07T04:50:36Z | |
| dc.description | For each pair (k,r) of positive integers with r>1, we consider an ideal I^(k,r)_n of the ring of symmetric polynomials in n variables. The ideal I_n^(k,r) has a basis consisting of Macdonald polynomials P(x_1,...,x_n;q,t) at t^{k+1}q^{r-1}=1, and is a deformed version of the one studied earlier in the context of Jack polynomials. In this paper we give a characterization of I^(k,r)_n in terms of explicit zero conditions on the k-codimensional shifted diagonals of the form x_{2}=tq^{s_1}x_1,...,x_{k+1}=tq^{s_k}x_k. The ideal I^(k,r)_n may be viewed as a deformation of the space of correlation functions of an abelian current of the affine Lie algebra \hat{sl_r}. We give a brief discussion about this connection. | |
| dc.description | Latex, 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209042 | |
| dc.identifier | http://arxiv.org/abs/math/0209042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64851 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.title | Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials | |
| dc.type | text |