与根系相关的正交多项式
Orthogonal polynomials associated with root systems
摘要：
设R和S是两个不可约的根系，它们跨越同一个向量空间，具有相同的外尔群W，使得S（但不一定R）是约化的.对于每个这样的对（R，S），我们构造了一族多元W-不变正交多项式，其系数是参数$q,t_1,t_2,...,t_r$的有理函数，其中r（= 1，2或3）是R中W-轨道的个数.对于这些参数的特定值，这些多项式给出了实和p-adic对称空间上的带状球函数的值。当R=S是$A_n$型时，它们也与I. G. Macdonald，对称函数和Hall多项式，第2版，牛津大学出版社（1995），第六章。
英文摘要：
Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal polynomials in several variables, whose coefficients are rational functions of parameters $q,t_1,t_2,...,t_r$, where r (=1,2 or 3) is the number of W-orbits in R. For particular values of these parameters, these polynomials give the values of zonal spherical functions on real and p-adic symmetric spaces. Also when R=S is of type $A_n$, they conincide with the symmetric polynomials described in I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford University Press (1995), Chapter VI.
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