Koszul duality and modular representations of semi-simple Lie algebras

Abstract

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the Lie algebra g of G can be endowed with a Koszul grading (extending results of Andersen, Jantzen and Soergel). We also give information about the Koszul dual rings. Our main tool is the localization theory in positive characteristic developed by Bezrukavnikov, Mirkovic and Rumynin.

85 pages, final (slightly condensed) version, to appear in DMJ

References in corpus (2)

• Noncommutative Counterparts of the Springer Resolution
• Linear Koszul duality and affine Hecke algebras

Cited by in corpus (24)

• Linear Koszul Duality
• Modular Koszul duality
• Geometricity for derived categories of algebraic stacks
• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Homological Projective Duality via Variation of Geometric Invariant Theory Quotients
• Representations of semisimple Lie algebras in prime characteristic and noncommutative Springer resolution
• Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
• Q-Koszul Algebras and Three Conjectures
• Linear Koszul Duality II - Coherent sheaves on perfect sheaves
• The homological projective dual of Sym^2 P(V)
• Modular affine Hecke category and regular centralizer
• Soergel bimodules and matrix factorizations
• Linear Koszul duality and affine Hecke algebras
• Categorification via blocks of modular representations for sl(n)
• Koszul duality and Frobenius structure for restricted enveloping algebras
• Canonical tilting relative generators
• Iwahori-Matsumoto involution and linear Koszul Duality
• Windows for cdgas
• Injectivity of a certain cycle map for finite dimensional W-algebras
• Koszul duality for Coxeter groups
• Hochschild cohomology of $U({\mathfrak{sl}}_2(k))$
• Loewy structure of $G_{1}T$-Verma modules of singular highest weights
• Singular blocks of restricted sl3
• Categorification via blocks of modular representations II