A coproduct structure on the formal affine Demazure algebra
Mathematische Zeitschrift, 282, no. 3-4, 2015, p. 1191-1218
(1st online appearance of the preprint on the 8-9-2012)
Kostant and Kumar have constructed a coproduct on a twisted group algebra, which, after dualization, gives an algebraic description of the equivariant Chow group (under the action of a maximal torus) of a variety of complete flags, i.e. a quotient of a split semi-simple linear algebraic group by a Borel subgroup. Their work also applies to K-theory.
Our text deals with the more general case of an oriented cohomology theory, with its associated formal group law. This formal group law is not assumed to be additive (as for Chow groups) or multiplicative (as for K-theory). We rely on the formalism of the previous publication Invariants, torsion indices and oriented cohomology of complete flags to show that most of Kostant and Kumar's ideas extend and the main statements sill hold in this more general setting, even though we use essentially different proofs. The reason is that important ingredients of the proofs of Kostant and Kumar are known to be false for theories with non additive and non multiplicative formal group laws, as discovered by Bressler and Evens.This article mainly deals with the algebraic definition and properties of the coproduct. It has two sequels, Push-pull operators on the formal Demazure algebra and its dual and Equivariant oriented cohomology of flag varieties in which it is shown that this algebraic construction indeed applies to the geometric setting of oriented cohomology theories and flag varieties.
