The elliptic Weyl character formula

TL;DR

This paper computes the equivariant elliptic cohomology of partial flag varieties for compact Lie groups, linking transfer maps to the Weyl-Kac character formula and advancing the elliptic Schubert calculus framework.

Contribution

It identifies the coefficients of equivariant elliptic cohomology as powers of Looijenga's line bundle and relates transfer maps to the Weyl-Kac character formula.

Findings

Identified RO(G)-graded coefficients as powers of Looijenga's line bundle.

Proved transfer along G/H to a point is given by the Weyl-Kac character formula.

Organized a theoretical framework for elliptic Schubert calculus.

Abstract

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].