论文标题
半神经谎言代数的模块化表达的尺寸
Dimensions of modular irreducible representations of semisimple Lie algebras
论文作者
论文摘要
在本文中，我们将kazhdan-lusztig类型的字符公式分类，以在一个较大的积极特征的领域上，以等位基因代数为单位代数。等效性是关于连接成分的组的组。字符计算以两个步骤完成。首先，我们处理杰出的$ p $ - 字符的情况：那些不包含在适当的利维中的情况。在这里，我们从本质上表明，我们认为的Equivariant模块的类别是仿射抛物线类别$ \ MATHCAL {O} $的单元格商。为此，我们证明了抛物面诱导的模块的两个分类与第一个命名作者猜想的仿射代数之间的等效性。对于一般的nilpotent $ p $ - 字符，我们通过在合适的Equivariant k-group上明确计算双重操作员来获得字符公式。
In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with respect to a group whose connected component is a torus. Character computation is done in two steps. First, we treat the case of distinguished $p$-characters: those that are not contained in a proper Levi. Here we essentially show that the category of equivariant modules we consider is a cell quotient of an affine parabolic category $\mathcal{O}$. For this, we prove an equivalence between two categorifications of a parabolically induced module over the affine Hecke algebra conjectured by the first named author. For the general nilpotent $p$-character, we get character formulas by explicitly computing the duality operator on a suitable equivariant K-group.
