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ON THE FORMAL AFFINE HECKE ALGEBRA

Part of: (Co)homology theory Representation theory of groups

Published online by Cambridge University Press:  09 June 2014

Changlong Zhong
Changlong Zhong*
Affiliation:
Fields Institute and University of Ottawa, Canada (zhongusc@gmail.com)
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Abstract

We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept called the normal formal group law, which we use to simplify the relations of the generators of the formal affine Demazure algebra and the formal affine Hecke algebra.

Keywords

formal group lawaffine Hecke algebraformal group algebra

MSC classification

Primary: 20C08: Hecke algebras and their representations 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 4 , October 2015 , pp. 837 - 855
Copyright
© Cambridge University Press 2014 

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References

Calmès, B., Petrov, V. and Zainoulline, K., Invariants, torsion indices and oriented cohomology of complete flags, Ann. Sci. Éc Norm. Supér. (4) 46(3) (2013), 405–448.Google Scholar
Calmès, B., Zainoulline, K. and Zhong, C., A coproduct structure on the formal affine Demazure algebra (arXiv:1209.1676).Google Scholar
Calmès, B., Zainoulline, K. and Zhong, C., Push-pull operators on the formal affine Demazure algebra and its dual (arXiv:1312.0019).Google Scholar
Chriss, N. and Ginzburg, V. , Representation Theory and Complex Geometry (Birkhäuser, Boston, 1997).Google Scholar
Demazure, M., Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287–301.Google Scholar
Ginzburg, V., Geometric methods in the representation theory of Hecke algebras and quantum groups. Notes by Vladimir Baranovsky, in Representation theories and algebraic geometry, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Volume 514, pp. 127–183 (Kluwer Acad. Publ., Dordrecht, 1998).CrossRefGoogle Scholar
Hoffmann, A., Malagón-López, J., Savage, A. and Zainoulline, K., Formal Hecke algebras and algebraic oriented cohomology theories, Selecta Math. to appear.Google Scholar
Kostant, B. and Kumar, S., The nil Hecke ring and cohomology of G∕P for a Kac-Moody group G ∗, Adv. Math. 62 (1986), 187–237.Google Scholar
Kostant, B. and Kumar, S., T-equivariant K-theory of generalized flag varieties, J. Differential Geometry 32 (1990), 549–603.CrossRefGoogle Scholar
Levine, M. and Morel, F., Algebraic cobordism, Springer Monographs in Mathematics (Springer, Berlin, 2007).Google Scholar
Lusztig, G., Cuspidal local systems and graded Hecke algebras. I, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 145–202.CrossRefGoogle Scholar
Malagón-López, J., Zainoulline, K. and Zhong, C., Invariants, exponents and formal group laws (arXiv:1207.1880).Google Scholar
Zhong, C., On the 𝛾-filtration of oriented cohomology of complete spin-flags, J. Pure Appl. Algebra 218(7) (2014), 1291–1301.Google Scholar