Invariants, torsion indices and oriented cohomology of complete flags, by Baptiste Calmes, Victor Petrov, and Kirill Zainoulline

In the present notes we generalize the classical work of Demazure [Invariants symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws.

Let G be a split semisimple linear algebraic group over a field and let T be its split maximal torus. We construct a generalized characteristic map relating the so called formal group ring of the character group of T with the cohomology of the variety of Borel subgroups of G. The main result of the paper says that the kernel of this map is generated by W-invariant elements, where W is the Weyl group of G.

As one of the applications we provide an algorithm (realized as a Macaulay2 package) which can be used to compute the ring structure of an oriented cohomology (algebraic cobordism of Levine-Morel, Morava K-theories, connective K-theory, Chow groups, etc.) of a complete flag variety.

Baptiste Calmes <>
Victor Petrov <>
Kirill Zainoulline <>