2013/01/12 by Nham V. Ngo, Ngo, Nham V.
Mathematics · #13Axx #20G05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.AC #math.RT #msc:13Axx #msc:20G05
paper · pdf · doi:10.48550/arxiv.1301.2712
extended version: the computation was extended for rank two Lie algebras, some result was generalized for simple classical Lie algebras. Note that the title was changed
openalex publication_date 2013/01/12 · arxiv created 2015/02/06 · arxiv updated 2015/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfrakg be a simple Lie algebra defined over an algebraically closed field k of characteristic p. Fix an integer r>1 and suppose that V1,…,Vr are irreducible closed subvarieties of \mathfrakg. Let C(V1,…,Vr) be the closed variety of all the pairwise commuting elements in V1×⋯× Vr. This paper studies the dimension and irreducibility of such varieties with various Vi in a Lie algebra \mathfrakg. In particular, we complete the problem for the case when Vi's are either Osub the closure of the subregular orbit or N the nilpotent cone of any rank two Lie algebra \mathfrakg. A result on the dimension of these mixed commuting varieties is generalized for higher ranks. Finally, we apply our calculations to study properties of support varieties for a simple module over the r-th Frobenius kernels of G.