论文标题
在扩展的重量上，单型及其在正交多项式上的应用
On the extended weight monoid and its applications to orthogonal polynomials
论文作者
论文摘要
给定一个仅连接的仅连接的半神经G组和连接的球形亚组K，我们基于G/K的均匀球形基准，确定了G/K的扩展重量单体的发电机。 令H为G的还原亚组，让P为H的抛物线亚组，G/P是球形的。带有此属性的三重（G，H，P）称为无多元系统，我们在（G，H）严格不可分解的情况下明确确定了G/P的扩展重量的发电机。 The extended weight monoid of G/P describes the induction from H to G of an irreducible H-representation V whose lowest weight is a character of P. The space of regular End(V)-valued functions on G that satisfy F(hgk)=hF(g)k for all h,k in H and all g in G, is a module over the algebra of H-biinvariant regular functions on G. We show that under a mild假设此模块是自由且有限生成的。结果，这种V型V的球形函数可以描述为基质值正交多项式的家族。
Given a connected simply connected semisimple group G and a connected spherical subgroup K we determine the generators of the extended weight monoid of G/K, based on the homogeneous spherical datum of G/K. Let H be a reductive subgroup of G and let P be a parabolic subgroup of H for which G/P is spherical. A triple (G,H,P) with this property is called multiplicity free system and we determine the generators of the extended weight monoid of G/P explicitly in the cases where (G,H) is strictly indecomposable. The extended weight monoid of G/P describes the induction from H to G of an irreducible H-representation V whose lowest weight is a character of P. The space of regular End(V)-valued functions on G that satisfy F(hgk)=hF(g)k for all h,k in H and all g in G, is a module over the algebra of H-biinvariant regular functions on G. We show that under a mild assumption this module is freely and finitely generated. As a consequence the spherical functions of such a type V can be described as a family of matrix-valued orthogonal polynomials.
