The elliptic Weyl character formula

We calculate equivariant elliptic cohomology of the partial flag variety $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}G/H$ , where $H⊆ G$ are compact connected Lie groups of equal rank. We identify the ${ RO}(G)$ -graded coefficients ${E} ll_G^*$ as powers of Looijenga’s line bundle and prove that transfer along the map $${equation*} π \,{:}\,G/H { pt} {equation*}$$ 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].