Andrei Zelevinsky

(Northeastern University)

Northeastern University

509 Lake Hall

3:00 p.m., Monday, March 29, 1999

Abstract: This is an account of a joint work in progress with Boris and Michael Shapiro, and Alek Vainshtein. We obtain a far-reaching generalization of the result due to Shapiro - Shapiro - Vainshtein who computed the number of connected components o f the variety of real upper unitriangular n x n matrices with non-vanishing "anti-principal" minors (i.e., minors that involve several initial rows and last columns of the matrix). They established a natural bijection between the connected components in question and the orbits of a certain linear group generated by symplectic transvection and acting on a vector space over the two-element field.

We extend this construction by associating such a group G to any pair of elements (u,v) in an arbitrary simply-laced Coxeter group W. If W is a (finite) Weyl group then the orbits of G enumerate the connected components of the so-called double Bruhat cell associated to (u,v).

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Web page: Alexandru I. Suciu	Created: March 16, 1999 Updated: March 23, 1999
Comments to: alexsuciu@neu.edu	URL: `http://www.math.neu.edu/~suciu/gas/zelevinsky-99.html`