Mathematics Seminar Series - Spring 2005

Monday, May 16, 2005
2:30 pm, Wheatley 1-057

Sangjib Kim

Yale University

Standard Monomial Theory for Flag Algebras

Abstract: Let G be the general linear group or the symplectic group over the complex number field, and U be its maximal unipotent subgroup. We study standard monomial theory of the ring of regular functions on G/U, called the flag algebra, using the philosophy of Gröebner bases and SAGBI bases combined with classical invariant theory. We describe the flag algebra in terms of Gelfand-Tsetlin patterns. In particular, we show that the flag algebra is a flat deformation of toric varieties.

The presentations cover a large variety of topics and are intended for a general math audience. The seminar is organized by Prof. Alfred Noël and we usually meet Monday afternoons, from 2:30 pm to 4:00 pm.

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