The elliptic Weyl character formula

We calculate equivariant elliptic cohomology of the partial flag variety G/H, where H \subseteq G are compact connected Lie groups of equal rank. We identify the RO(G)-graded coefficients Ell_G^* as powers of Looijenga’s line bundle and prove that transfer along the map {\pi}: G/H -\rightarrow 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].