Combinatorial aspects of the linkage principle for general linear supergroups

Abstract

Let $G=GL(m|n)$ be a general linear supergroup and $G_{ev}$ be its even subsupergroup isomorphic to $GL(m)\times GL(n)$. In this paper we use the explicit description of $G_{ev}$-primitive vectors in the costandard supermodule $\nabla (\lambda )$, the largest polynomial $G$-subsupermodule of the induced supermodule $H_G^0(\lambda )$, for $(m|n)$-hook partition $\lambda$, and a properties of certain morphisms ${\psi }_k$ to derive results related to the odd linkage for $G$ over a field $F$ of characteristic different from $2$.

References in corpus (1)

• A new proof of the Mullineux conjecture