Critical-weight theta-block conjecture for intermediate Lie algebras

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 the source. A Jacobi form is said to have critical weight when its weight is the critical weight determined by the corresponding intermediate algebra. Critical-weight theta-block conjecture. The theta blocks associated with the intermediate Lie algebras in the intermediate exceptional series are holomorphic Jacobi forms of critical weight. The source presents this as a proposed extension of the correspondence between semisimple Lie algebras and holomorphic theta blocks of singular weight; the assertion remains unproved in the supplied text.