HAL CCSD
Push-pull operators on the formal affine Demazure algebra and its dual
Calmès, Baptiste
Zainoulline, Kirill
Zhong, Changlong
Laboratoire de Mathématiques de Lens (LML) ; Université d'Artois (UA)
Department of Mathematics and Statistics [Ottawa] ; University of Ottawa [Ottawa]
25 pages
hal-00922509
https://univ-artois.hal.science/hal-00922509
https://univ-artois.hal.science/hal-00922509
2013
ARXIV: 1312.0019
info:eu-repo/semantics/altIdentifier/arxiv/1312.0019
en
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal affine Demazure algebra which serves as an algebraic counterpart of the natural pairing on the T-equivariant oriented cohomology of G/B induced by multiplication and push-forward to a point. This paper can be viewed as the next step towards the 'algebraization program' for equivariant oriented cohomology theories started in arXiv:0905.1341 and continued in arXiv:1208.4114 and arXiv:1209.1676; the general idea being to match cohomology rings of algebraic varieties and elements of classical interest in them (such as classes of Schubert varieties) with algebraic and combinatorial objects that can be introduced in the spirit of [Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21:287-301, 1973] and [Kostant, Kumar, The nil Hecke ring and cohomology of G/P for a Kac-Moody group G, Advances in Math. 62:187-237, 1986].
2013-11-29