Standard monomial theory for G2

Abstract

Let G be a semi-simple algebraic group and B a Borel subgroup. Let X be a Schubert variety in G/B. Let L be an ample line bundle on G/B, as well as its restriction to X. A standard monomial theory for Schubert varieties in G/B is developed in [9], [11], [8], [10] as a generalization of the classical Hodge-Young theory (cf [3],[4]). This theory consists in the construction of a characteristic-free basis for H0 (X,L). This theory is extended to Schubert varieties in the infinite dimensional flag variety ŜLn/B in [13] (see also [12]). In this paper, we extend the theory to Schubert varieties in the infinite dimensional flag variety Ŝp2n/B.