Formal Hecke algebras and algebraic oriented cohomology theories

• Alex Hoffnung ^[1] ; José Malagón-López ^[2] ; Alistair Savage ^[3] ; Kirill Zainoulline ^[3]
  1. [1] Temple University

     Temple University

     City of Philadelphia, Estados Unidos

     
  2. [2] University of Toronto

     University of Toronto

     Canadá

     
  3. [3] University of Ottawa

     University of Ottawa

     Canadá

     

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 4, 2014, págs. 1213-1245
• Idioma: inglés
• DOI: 10.1007/s00029-014-0169-3
• Enlaces
  • Texto completo
• Resumen

  • In the present paper, we generalize the construction of the nil Hecke ring of Kostant–Kumar to the context of an arbitrary formal group law, in particular, to an arbitrary algebraic oriented cohomology theory of Levine–Morel and Panin–Smirnov (e.g., to Chow groups, Grothendieck’s K0K0 , connective KK -theory, elliptic cohomology, and algebraic cobordism). The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings, respectively. We also introduce a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra, respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.