Nora Ganter

SYMMETRIC AND EXTERIOR POWERS OF CATEGORIES

We define symmetric and exterior powers of categories, fitting into categorified Koszul complexes. We discuss examples and calculate the effect of these power operations on the categorical characters of matrix 2-representations.

The elliptic Weyl character formula

We calculate equivariant elliptic cohomology of the partial flag variety G/H, where H ⊆ G are compact connected Lie groups of equal rank. We identify the RO(G)-graded coefficientsEll ∗ G as powers of Looijenga’s line bundle and prove that transfer along the map �: 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 [GR].

The Jacobi orientation and the two-variable elliptic genus

We explain the relationship between the sigma orientation and Witten genus on the one hand and the two-variable elliptic genus on the other. We show that if E is an elliptic spectrum, then the Theorem of the Cube implies the existence of canonical SU-orientation of the associated spectrum of Jacobi forms. In the case of the elliptic spectrum associated to the Tate curve, this gives the two-variable elliptic genus. We also show that the two-variable genus arises as an instance of the circle-equivariant sigma orientation.