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SUMMARY:Angel Roman (William & Mary)
DTSTART:20210407T190000Z
DTEND:20210407T200000Z
DTSTAMP:20260420T052909Z
UID:NYC-NCG/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/52/"
 >The Mackey bijection for reductive groups and continuous fields of reduce
 d group C*-algebras</a>\nby Angel Roman (William & Mary) as part of Noncom
 mutative geometry in NYC\n\n\nAbstract\nIn the 1970's\, George Mackey prop
 osed that there should be some kind of analogy between unitary representat
 ions of semisimple groups $G$ and unitary representations of its  Cartan m
 otion group $G_0=K\\ltimes \\mathfrak{g}/\\mathfrak{k}$\, where $K$ is a m
 aximal compact subgroup of $G$. Eventually a precise bijection was constru
 cted between the irreducible tempered unitary representations of $G$ and t
 he irreducible unitary representations of $G_0$. In a joint work with Nige
 l Higson we characterized the Mackey bijection using continuous fields of 
 reduced group $C^*$-algebra of complex reductive group. We constructed an 
 embedding between the reduced $C^*$-algebras of $G_0$ and $G$. Time permit
 ting\, I will discuss ongoing work (with Nigel Higson and Pierre Clare) to
 ward a generalization to a wider class of groups.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/52/
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