Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials
Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials
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DOI：
10.1155/s1073792803209119
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发表时间：
2002-09
期刊：
影响因子：
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通讯作者：
B. Feigin;M. Jimbo;T. Miwa;E. Mukhin
中科院分区：
文献类型：
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作者：
B. Feigin;M. Jimbo;T. Miwa;E. Mukhin
对于每对具有r>；1的正整数(k，r)，我们考虑n元对称多项式环的理想i^(k，r)_n。理想I_n^(k，r)在t^{k+1}q^{r-1}=1时有一个由Macdonald多项式P(x_1，…，x_n；q，t)组成的基，它是先前在Jack多项式的背景下研究的变形形式。本文给出了形如x_{2}=tq^{S_1}x_1，…，x_{k+1}=t_q^{S_k}x_k的k维余维移对角线上的显式零条件刻画了i^(k，r)_n，理想的i^(k，r)_n可以看作是仿射李代数的阿贝尔流的相关函数空间的变形。我们对这一联系进行了简要的讨论。
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.