关于最高权范畴中的极小倾斜复形

Pub Date : 2022-12-22 DOI:10.1007/s10468-022-10188-5

Jonathan Gruber

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引用次数: 0

摘要

我们解释了最高权重类别对象的最小倾斜复数的构造，并详细研究了标准对象和简单对象的最小倾斜复数。对于复简单李代数、仿射 Kac-Moody 代数和单根量子群的某些表示范畴，我们将这些复数项中出现的不可分解倾斜对象的乘数与卡兹丹-卢兹蒂格多项式的系数联系起来。

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On Minimal Tilting Complexes in Highest Weight Categories

We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie algebras, affine Kac-Moody algebras and quantum groups at roots of unity, we relate the multiplicities of indecomposable tilting objects appearing in the terms of these complexes to the coefficients of Kazhdan-Lusztig polynomials.

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