CANONICAL BASES AND STANDARD MONOMIALS

Let U be the quantized enveloping algebra associated to a simple Lie a lgebra g by Drinfel'd and Jimbo. Let lambda be a classical fundamental weight for g, and V(lambda) the irreducible, finite-dimensional type 1 highest weight U-module with highest weight lambda. We show that the canonical basis for V(lambda) (see Kashiwara [6, 0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, 2.4 and 2.5]) for V(lambda) coincide.