Blocks and characters of $D(2\mathrm{\mid }1;\zeta )$-modules of non-integral weights

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