Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebras $D(2|1;\zeta )$

Abstract

We establish character formulae for representations of the one-parameter family of simple Lie superalgebras $D(2|1;\zeta )$. We provide a complete description of the Verma flag multiplicities of the tilting modules and the projective modules in the BGG category $\mathcal{O}$ of $D(2|1;\zeta )$-modules of integral weights, for any complex parameter $\zeta$. The composition factors of all Verma modules in $\mathcal{O}$ are then obtained.

36 pages, final version, to appear in Transformation Groups

References in corpus (1)

• Type C blocks of super category O

Cited by in corpus (4)

• Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$
• Odd singular vector formula for general linear Lie superalgebras
• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebra $G(3)$
• Modular representations of exceptional supergroups