Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of the group. They are isomorphic with the equivariant intersection cohomology of affine Schubert varieties, endowing the latter with a new ring structure. Study of the finer aspects of the structure of the big algebras will also furnish the stalks of the intersection cohomology with ring structure, thus ringifying Lusztig’s q -weight multiplicity polynomials i.e., certain affine Kazhdan–Lusztig polynomials.

中文翻译：

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半单李群表示的交换化身


在这里，我们宣布基里洛夫代数的大交换子代数的构造和性质，该子代数附加到复杂半简单李群的有限维不可约表示。它们是群分类空间上同调的交换有限平坦代数。它们与仿射舒伯特簇的等变交上同构同构，赋予后者新的环结构。对大代数结构的更精细方面的研究还将提供与环结构的交上同调的茎，从而环化Lusztig的q权重多项式，即某些仿射Kazhdan-Lusztig多项式。