The Mackey bijection for reductive groups and continuous fields of reduced group C*-algebras

Angel Roman (William & Mary)

07-Apr-2021, 19:00-20:00 (3 years ago)

Abstract: In the 1970's, George Mackey proposed that there should be some kind of analogy between unitary representations of semisimple groups $G$ and unitary representations of its Cartan motion group $G_0=K\ltimes \mathfrak{g}/\mathfrak{k}$, where $K$ is a maximal compact subgroup of $G$. Eventually a precise bijection was constructed between the irreducible tempered unitary representations of $G$ and the irreducible unitary representations of $G_0$. In a joint work with Nigel 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 permitting, I will discuss ongoing work (with Nigel Higson and Pierre Clare) toward a generalization to a wider class of groups.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )


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