Invariants, torsion indices and oriented cohomology of complete flags

By B. Calmès, V. Petrov, K. Zainoulline. 2009

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In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple 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 Macaulau2 package) which can be used to compute the ring structure of an oriented cohomology (algebraic cobordism, Morava $K$-theories, connective K-theory, Chow groups, K_0, etc.) of a complete flag variety.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f6c066d0dfb3f3746ca0f87c718100052af6f7f