Character formulae and a realization of tilting modules for sl2[t]sl2[t]

In this paper we study the category of graded modules for the current algebra associated to sl2sl2. The category enjoys many nice properties, including a tilting theory which was established in [1]. We show that the indecomposable tilting modules for sl2[t]sl2[t] are the exterior powers of the fundamental global Weyl module and give the filtration multiplicities in the standard and costandard filtration. An interesting consequence of our result (which is far from obvious from the abstract definition) is that an indecomposable tilting module admits a free right action of the ring of symmetric polynomials in finitely many variables. Moreover, if we go modulo the augmentation ideal in this ring, the resulting sl2[t]sl2[t]-module is isomorphic to the dual of a local Weyl module.