Invariants of the adjoint action in the nilradical of a parabolic subalgebra of types Bn, Cn, Dn

2012/03/14 by Victoria Sevostyanova, Sevostyanova, Victoria
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1203.3001

openalex publication_date 2012/03/14 · arxiv created 2012/05/14 · arxiv updated 2012/05/15 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We study invariants of the adjoint action of the unipotent group in the nilradical of a parabolic subalgebra of types Bn, Cn, Dn. We introduce the notion of expanded base in the set of positive roots and construct an invariant for every root of the expanded base. We prove that these invariants are algebraically independent. We also give an estimate of the transcendence degree of the field of invariants.

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