Regular Functions on Certain Infinite-dimensional Groups
In the paper , 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).
KeywordsRegular Function Finite Type Coordinate Ring Bruhat Order Flag Variety
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