The nil Hecke Ring and Cohomology of G/P for a Kac--Moody group G
Abstract
Let G be the group with Borel subgroup B, associated to a Kac-Moody Lie algebra [unk] (with Weyl group W and Cartan subalgebra [unk]). Then H*(G/B) has, among others, four distinguished structures (i) an algebra structure, (ii) a distinguished basis, given by the Schubert cells, (iii) a module for W, and (iv) a module for Hecke-type operators Aw, for w [unk] W. We construct a ring R, which we refer to as the nil Hecke ring, which is very simply and explicitly defined as a functor of W together with the W-module [unk] alone and such that all these four structures on H*(G/B) arise naturally from the ring R.
- Publication:
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Proceedings of the National Academy of Science
- Pub Date:
- March 1986
- DOI:
- Bibcode:
- 1986PNAS...83.1543K