# Formal Hecke algebras and oriented cohomology theories

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Mathieu Stiénon, Nigel Higson, Ping Xu.

**Speaker:** Alexander Hoffnung, Temple

**Abstract:** The affine Hecke algebra can be constructed geometrically on the
equivariant K-theory of the Steinberg variety. Many related
convolution constructions appear in geometric representation on
various (co)homology theories. It seems natural to work towards a
theory of higher representation theory in order to find a unified
framework for such geometric constructions.
We implement formal methods to study the role of arbitrary oriented
cohomology theories in analogues of geometric constructions in
representation theory. We generalize the construction of the nil Hecke
ring of Kostant and Kumar to the context of an arbitrary oriented
cohomology theory of Levine and Morel, e.g. to Chow groups, connective
K-theory, elliptic cohomology, or algebraic cobordism.
In particular, we define formal (affine) Demazure algebras and formal
(affine) Hecke algebras. These depend on one-dimensional commutative
formal group laws and specialize to known variants of the Hecke
algebra at the additive and multiplicative formal group laws. In
general, this family of formal Hecke algebras satisfies equations that
we call Â´oriented braid relationsÂ´, which agree with the usual braid
relations at the additive and multiplicative formal group laws.
Joint work w. JosÃ© MalagÃ³n Lopez, Alistair Savage, and Kirill Zainoulline

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 11/13/2012

**Time:** 2:30pm - 3:30pm