Regular Functions on Certain Infinite-dimensional Groups

  • Victor G. Kac
  • Dale H. Peterson
Part of the Progress in Mathematics book series (PM, volume 36)

Abstract

In the paper [18], we began a detailed study of the “smallest” group G associated to a Kac-Moody algebra g(A) and of the (in general infinite-dimensional) flag varieties Pν Λ associated to G. In the present paper we introduce and study the algebra F[G] of “strongly regular” functions on G. We establish a Peter-Weyl-type decomposition of F[G] with respect to the natural action of G × G (Theorem 1) and prove that F[G] is a unique factorization domain (Theorem 3).

Keywords

Regular Function Finite Type Coordinate Ring Bruhat Order Flag Variety 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Victor G. Kac
    • 1
  • Dale H. Peterson
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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