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).
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To Igor Rostislavovich Shafarevich on his 60th birthday
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Kac, V.G., Peterson, D.H. (1983). Regular Functions on Certain Infinite-dimensional Groups. In: Artin, M., Tate, J. (eds) Arithmetic and Geometry. Progress in Mathematics, vol 36. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-9286-7_8
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DOI: https://doi.org/10.1007/978-1-4757-9286-7_8
Publisher Name: Birkhäuser, Boston, MA
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