Classification problem of hypergeometric differential systems

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With support of many examples with a computer, and by communication with world-wide experts in several fields, we obtained the following results.Mutsumi Saito generalized the classification theorem of A-hypergeometric systems to the cases when A is inhomogeneous and/or when we work in the analytic category. He also gave a dimension formula for the log-free series solutions when A is homogeneous, and a rank formula and the proof of the equivalence of Cohen-Macaulayness with the condition that the ranks are the same at all parameters, when A is homogeneous, and the convex hull of A is a simplex.Hiroshi Yamashita obtained some results useful to know when an isotropy representation is irreducible. Furthermore he systematically constructed nonzero quotient representations of isotropy representations attached to discrete series.Keiji Matsumoto clarified a pairing between twisted cohomology groups associated with generalized Airy functions. Writting a base of twisted cohomology groups by Young diagrams, he showed that for the base, the pairing can be explicitly written by skew-Schur polynomials.Youichi Shibukawa solved the classification problem for R operators.For the simplest affine Lie algebra A_1^<(1)> , using two of its realizations, Hiro-Fumi Yamada discovered the weight vectors are written by a modular version of Schur functions and Schur's Q-functions respectively.Akihito Wachi has studied the structure of generalized Verma modules, in particular, their irreducibility, emphasizing their relations with invariant functions.