A Morita theorem for modular finite W-algebras

2015/05/14 by Topley, Lewis
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1505.03896

Abstract

We consider the Lie algebra \mathfrakg of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent orbit O ⊆ \mathfrakg we choose a representative e∈ O and attach a certain filtered, associative algebra \widehatU(\mathfrakg,e) known as a finite W-algebra, defined to be the opposite endomorphism ring of the generalised Gelfand-Graev module associated to (\mathfrakg, e). This is shown to be Morita equivalent to a certain central reduction of the enveloping algebra of U(\mathfrakg). The result may be seen as a modular version of Skryabin's equivalence.

Related

• Modular finite W-algebras
• Finite W-superalgebras for basic Lie superalgebras
• Finite-dimensional representations of minimal nilpotent W-algebras and\n zigzag algebras
• On Gelfand-Kirillov conjecture for some W-algebras
• Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras