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General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
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Combinatorics of totally positive matrices S. V. Fominab a SPIIRAS b U. Michigan – M.I.T. |
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Abstract: A matrix is called totally positive if all its minors are positive. How many minors of an These questions are related to the problem of factoring an invertible square matrix into the minimal number of “elementary factors”. The solutions involve combinatorics of reduced words and pseudo-line arrangements, together with a family of biregular automorphisms of “double Bruhat cells” in the general linear group. This is joint work with Andrei Zelevinsky. |