Blocks and characters of $D(2|1;\zeta )$-modules of non-integral weights

Abstract

We classify blocks in the BGG category $\mathcal{O}$ of modules of non-integral weights for the exceptional Lie superalgebra $D(2|1;\zeta )$. We establish various reduction methods, which connect some types of non-integral blocks of $D(2|1;\zeta )$ with integral blocks of general linear Lie superalgebras $\mathfrak{gl}(1|1)$ and $\mathfrak{gl}(2|1)$. We compute the characters for irreducible $D(2|1;\zeta )$-modules of non-integral weights in $\mathcal{O}$.

arXiv comment27 pages. The reference has been corrected in this version