The elliptic Weyl character formula

Abstract

We calculate equivariant elliptic cohomology of the partial ag variety G/H, where H ⊆ G are compact connected Lie groups of equal rank. We identify the RO(G)-graded coefficients εll∗G as powers of Looijenga's line bundle and prove that transfer along the map φ :G/H → pt is calculated by the Weyl-Kac character formula. Treating ordinary cohomology, K-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram, Elliptic Schubert calculus, in preparation].