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Mathematics Colloquium


Date:  Tuesday, April 04, 2006

Title:  The cone of effective weights for quivers and Horn type problems

Abstract:  In 1912, H. Weyl asked for a description of the eigenvalues of a sum of two Hermitian matrices in terms of the eigenvalues of the summands. In 1962, A. Horn recursively constructed a list of inequalities for the eigenvalues of two Hermitian matrices and their sum, which he conjectured to be necessary and sufficient. In 2000 Horn's conjecture was finally proved. Several other problems turn out to be related and have the exact same answer as Weyl's eigenvalue problem, including the non-vanishing of the Littlewood-Richardson coefficients and the existence of short exact sequences of finite abelian p-groups. Using methods from quiver invariant theory, we obtain a list of necessary and sufficient inequalities for the existence of long exact sequences of m finite abelian p-groups. We explain how this result is related to some generalized Littlewood-Richardson coefficients and eigenvalues of Hermitian matrices satisfying certain (in)equalities.

Speaker:  Calin Chindris
Institution:  University of Minnesota


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