The University of Michigan Combinatorics Seminar
In the talk, we will construct three complex diagonalizable matrices B, C, and A=B+C of special spectral types associated to Simpson's classification. When the eigenvalues of A, B, and C are real, we construct a Hermitian form such that A, B, and C are self-adjoint with respect to the form. Then we find inequalities on the eigenvalues of A, B, and C, which make the form positive-definite. Then we will discuss applications of the above to the Littlewood-Richardson rule, geometry/combinatorics of varieties of triple flags, (Fuchsian) systems of differential equations, and generalized hypergeometric functions.