Finite Order Automorphisms and a Parametrization of Nilpotent Orbits in p-adic Lie Algebras.

[摘要] Let k be a field with a nontrivial discrete valuation which is complete and has perfectresidue field. Let G be the group of k-rational points of a reductive, linear algebraicgroup G equipped with a finite cyclic group L acting on G by algebraic automorphismsdefined over k: We assume that the Lie algebra of G decomposes into a directsum of eigenspaces, which we denote by g^i; under the action of L. If H is a k-subgroupof G^L, the group of L-fixed points, which contains the neutral component of G^L; thenH = H(k) acts on each eigenspace of g; Let r in R: Under mild restrictions on theresidual characteristic of k; the set of nilpotent H-orbits in the 1-eigenspace g^1 isparametrized by equivalence classes of noticed Moy-Prasad cosets of depth r whichlie in g^1.

[发布机构] University of Michigan

[效力级别] Bruhat-tits Theory

[关键词] Group Theory;Bruhat-tits Theory;Mathematics;Science;Mathematics