Joint seminar: Combinatorics and Lie Groups

Totally non negative and oscillatory elements in semi-simple groups

Andrei Zelevinsky

Northeastern University

Febrary 10,
refreshments at 3:45pm


A matrix is totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative) real numbers. The first systematic study of these matrices was undertaken in the 1930s by F.R. Gantmacher and M.G. Krein. More recently, G. Lusztig discovered a surprising connection between total positivity and canonical bases for quantum groups, and extended the subject by defining totally positive and totally nonnegative elements for any semisimple group. We shall discuss some classical results about total positivity, and how to extend them to arbitrary semisimple groups. Most of the new results to be discussed were obtained jointly with S. Fomin.

Speaker's Contact Info: andrei(at-sign)

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