A Construction of Representations of Loop Groups.

The operators Tnf(x) =
Pn
i=1 f( 1
nx+ i
n) map periodic functions
f(x+1) = f(x) to periodic functions and satisfy TmTn = Tmn. They form a
part of Bost-Connes system. In this talk, we show that the generalizations of
Tn give arise to representations of GLn over p-adic elds and representations
of loop group GLn over local elds.
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This talk is supported by the Mrs. Hepsa Ely Silliman Memorial Fund