Linkage principle for ortho-symplectic supergroups

TL;DR

This paper establishes a linkage principle for modular representations of ortho-symplectic supergroups, extending the understanding of their representation theory in positive characteristic.

Contribution

It derives the linkage principle for orthosymplectic supergroups by analyzing the Frobenius thickening and flag structures, building on Doty's approach.

Findings

Derived strong linkage for Frobenius thickening $G_rT$ of $OSP(2|1)$.

Established the linkage principle for $SpO(2m|2n+1)$ and $SpO(2m|2n)$ supergroups.

Abstract

The purpose of the paper is to derive linkage principle for modular representations of ortho-symplectic supergroups. We follow the approach of Doty and investigate in detail the representation theory of the orthosymplectic group $OSP(2|1)$ and that of its Frobenius thickening. Using the description of flags and adjacent Borel supersubgroups we derive first the strong linkage for the Frobenius thickening $G_rT$ of the orthosymplectic supergroup $G$ of type $SpO(2m|2n+1)$ and $SpO(2m|2n)$. Based on this, we derive the linkage principle for orthosymplectic supergroup $SpO(2m|2n+1)$ and $SpO(2m|2n)$.