2020/05/20 by Roman Bezrukavnikov, Bezrukavnikov, Roman, Ivan Losev +1
Mathematics · #17B20 #17B35 #17B50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2005.10030
openalex publication_date 2020/05/20 · openalex created_date 2023/03/17 · openalex updated_date 2026/07/28
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 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.