Dimensions of modular irreducible representations of semisimple Lie algebras
Dimensions of modular irreducible representations of semisimple Lie algebras
复制标题
半单李代数模不可约表示的维数
DOI：
--
复制
发表时间：
2020
影响因子：
3.9
通讯作者：
I. Losev
中科院分区：
文献类型：
--
作者：
R. Bezrukavnikov;I. Losev
在本文中，我们对大正特征域上还原代数群的李代数的等变不可约表示进行了分类并给出了 Kazhdan-Lusztig 型特征公式。等方差是相对于其连通分量是环面的群而言的。字符计算分两步完成。首先我们来对待特殊的情况
p
p
-字符：那些不包含在适当的 Levi 中的字符。在这里，我们本质上表明，我们考虑的等变模块的类别是仿射抛物线类别的单元商
氧
数学{O}
。为此，我们证明了第一作者猜想的仿射赫克代数上抛物线诱导模的两个分类之间的等价性。对于一般幂幂
p
p
-字符，我们通过在合适的等变 K 群上显式计算对偶运算符来获得字符公式。
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
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
O
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
p
-character, we get character formulas by explicitly computing the duality operator on a suitable equivariant K-group.