论文标题
模块化Weyl-kac特征公式
The modular Weyl-Kac character formula
论文作者
论文摘要
我们对抗球形Hecke类别的不可约定的分级表示分类并明确构建了一个程度。这些同质表示中的每一个都是一维的，可以通过涉及该类别的每个（无限维）标准表示的BGG分辨率来共同构建。因此，我们确定了一个任意Coxeter组和任意抛物线子组的逆抛物线$ P $ -KAZHDAN--LUSZTIG矩阵的完整第一行。这将Weyl-kac字符公式概括为所有Coxeter系统（及其抛物面），并证明了这种广义公式相对于对任意领域的基础变化而言是刚性的。
We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated in one degree. Each of these homogeneous representations is one-dimensional and can be cohomologically constructed via a BGG resolution involving every (infinite dimensional) standard representation of the category. We hence determine the complete first row of the inverse parabolic $p$-Kazhdan--Lusztig matrix for an arbitrary Coxeter group and an arbitrary parabolic subgroup. This generalises the Weyl--Kac character formula to all Coxeter systems (and their parabolics) and proves that this generalised formula is rigid with respect to base change to an arbitrary field.
