Splitting quasireductive supergroups and volumes of supergrassmannians
Abstract
We introduce the notion of splitting subgroups of quasireducitve supergroups, and explain their significance. For $GL(m|n)$, $Q(n)$, and defect one basic classical supergroups, we give explicit splitting subgroups. We further prove they are minimal up to conjugacy, except in the $GL(m|n)$ case where it remains a conjecture. A key tool in the proof is the computation of the volumes of complex supergrassmannians, which is of interest in its own right.
Fields of Study & Subjects
Advanced Algebra and Geometry
Finite Group Theory Research
Advanced Topics in Algebra
Publication details
- Journal / source
- Algebraic Geometry and Physics
- Publisher
- International Press of Boston
- Volume
- 3
- Issue
- 1
- Pages
- 81–117
- Publication date
- 1 January 2026
- Language
- EN