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Summary: POWER OPERATIONS IN ELLIPTIC COHOMOLOGY AND
REPRESENTATIONS OF LOOP GROUPS
MATTHEW ANDO
Abstract. The first part describes power operations in elliptic cohomology in
terms of isogenies of the underlying elliptic curve. The second part discusses
a relationship between equivariant elliptic cohomology and representations of
loop groups. The third part investigates the representation theoretic consid-
erations which give rise to the power operations discussed in the first part.
Contents
Introduction 2
Part I. Power operations and elliptic cohomology 6
1. Complex-orientable cohomology theories 6
2. Elliptic cohomology theories 10
3. Uniqueness and integrality using Hopf rings 15
4. Drinfel'd Isogenies 18
5. Unstable operations from homomorphisms of formal groups 20
6. Examples 22
Part II. Elliptic cohomology and loop groups 28
7. Notation 28
8. Equivariant elliptic cohomology 29
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