A new approach to standard monomial theory for classical groups

Abstract

We describe a procedure for constructing monomial bases for finite dimensional irreducible representations of complex semisimple Lie algebras. A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elements γ, α, α a simple root, in the opposite Borel subalgebra. As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups.