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Exposé Bourbaki 828 : Dunkl operators

Exposé Bourbaki 828 : Dunkl operators

Gerrit J. HECKMAN
Exposé Bourbaki 828 : Dunkl operators
  • Année : 1997
  • Tome : 245
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 20G05, 22E46, 33C70
  • Pages : 223-246
  • DOI : 10.24033/ast.394

Elementary spherical functions on semisimple Lie groups suggest by “variation of structural parameters” the concept of hypergeometric functions associated with root systems. Such a theory was developped several years ago by Opdam and the lecturer. Dunkl operators are a mixture of differential and divided difference operators, and they form a basic tool in the differential algebra of this hypergeometric theory. It is remarkable to see the ubiquitous role played by the representation theory of affine Hecke algebras and their degenerations

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