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

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