4 problems

Let $\mathfrak{g}_I$ be an intermediate Lie algebra between $\mathfrak{g}_1$ and $\mathfrak{g}_2$, and let the associated theta block be constructed from the positive roots and wei…

For each intermediate Lie algebra in the intermediate exceptional series, form the theta block from its associated positive roots and weights, using the construction described in t…

Let $N$ be a positive integer, and let $\phi$ be a holomorphic Jacobi form whose Gritsenko lift is a Borcherds product. A pure theta block is a theta block whose defining function…

Let $L$ be the lattice indexing the Jacobi-form space $J_{k,L,1}$, and let $\phi\in J_{k,L,1}$. Let $T_{-}(2)$ denote the index-raising Hecke operator, and let…