Toward a Holographic Transform for the Quantum Clebsch-Gordan Formula

Abstract: A holographic transform is an equivariant map which increases the number of variables in its domain, a space of functions. The tensor product of two finite dimensional irreducible representations of the Lie algebra $\mathfrak{sl}(2)$ decomposes into a direct sum of irreducible modules. In fact, the tensor product of representations of $U_q(\mathfrak{sl}(2))$, the quantum analogue of $\mathfrak{sl}(2)$, decomposes in the same way. The purpose of this talk will be discussing the search for explicit holographic transforms associated with these decompositions.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasprobabilityquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the discipline

GAG seminar

Series comments: Description: Non-specialized research seminar