Minimal Nilpotent Orbits of type D and E

2025/01/16 by Boming Jia, Jia, Boming
Engineering · Mathematics · #20G05 #FOS: Mathematics #Mathematics and Applications #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2501.12406

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first show the closure of the minimal nilpotent adjoint orbit Omin^D_n in so_2n is isomorphic to the affinization of T^*(SL_n-1/[P,P]) where P is the parabolic subgroup P_(1,1,n-3) of SL_n-1(C). Then we prove that the closure of the minimal nilpotent adjoint orbit Omin^E₆ of the complex simple Lie algebra E₆ is isomorphic to the affinization of T^*(SL₄/P^u) where P^u is the unipotent radical of the parabolic subgroup P_(2,2) of SL₄(\C). In the end we will formulate a similar result for type E₇.

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