Monday, May 16th, 2005
2:30pm - 3:30pm, in 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.