TL;DR
This paper investigates the structure and basis of the formal affine Hecke algebra acting on the formal group algebra, introducing the concept of the normal formal group law to simplify algebraic relations.
Contribution
It provides a basis for the formal affine Hecke algebra over the formal group algebra and introduces the normal formal group law to streamline algebraic relations.
Findings
The formal affine Hecke algebra has a basis indexed by the Weyl group.
Introduction of the normal formal group law simplifies algebraic relations.
The action of the algebra on the formal group algebra is characterized.
Abstract
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept called the normal formal group law, which we use to simplify the relations of the generators of the formal affine Demazure algebra and the formal affine Hecke algebra.
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