Monodromy of the hypergeometric differential equation of type (3,6) II. The unitary reflection group of order $2^9 . \: 3^7 . \: 5 . \: 7$

Keiji Matsumoto; Takeshi Sasaki; Nobuki Takayama; Masaaki Yoshida

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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....