| We study standard monomial theory of the flag algebra for the general linear group and the symplectic group using the philosophy of Grobner bases and SAGBI bases combined with classical invariant theory. If G is one of these groups, and UG is a maximal unipotent subgroup, then we describe R (G/UG), the ring of regular functions on G/UG, in terms of Gelfand-Tsetlin patterns. In particular, we show that R (G/UG) is a flat deformation of a toric variety defined in terms of Gelfand-Tsetlin patterns. |
