The University of Michigan Combinatorics Seminar


Abstract 

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 selfadjoint with respect to the form. Then we find inequalities on the eigenvalues of A, B, and C, which make the form positivedefinite. Then we will discuss applications of the above to the LittlewoodRichardson rule, geometry/combinatorics of varieties of triple flags, (Fuchsian) systems of differential equations, and generalized hypergeometric functions. 