Littelmann paths for the basic representation of an affine Lie algebra

Abstract

A highest-weight representation of an affine Lie algebra g ˆ can be modeled combinatorially in several ways, notably by the semi-infinite paths of the Kyoto school and by Littelmann's finite paths. In this paper, we unify these two models in the case of the basic representation of an untwisted affine algebra, provided the underlying finite-dimensional algebra g possesses a minuscule representation (i.e., g is of classical or E 6 , E 7 type). We apply our “coil model” to prove that the basic representation of g ˆ , when restricted to g , is a semi-infinite tensor product of fundamental representations, and certain of its Demazure modules are finite tensor products.