2022/06/15 by Serganova, Vera, Sherman, Alexander · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2206.07693
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.