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Regular, Quasi-regular and Induced representations of infinite-dimensional groups

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Alexander Kosyak
Institute of Mathematics of NAS of Ukraine, Kiev/MPIM
Die, 2019-02-12 14:00 - 15:00
MPIM Lecture Hall

Almost all harmonic analysis on locally compact groups is based on the existence (and uniqueness)
of the Haar measure. If the group is not locally compact there is no Haar measure on it. The  aim
of the talk is
to give a systematic development, by example, of noncommutative harmonic 
analysis on infinite-dimensional (non-locally compact) matrix groups.

We generalize the notion of regular, quasi-regular and induced
representations to arbitrary
infinite-dimensional groups. In order to do  so,  we replace the non-existing Haar measure on an 
infinite-dimensional group by a suitable quasi-invariant measure on an appropriate completion
of the initial group or on the completion of a homogeneous space.

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