Date Thesis Awarded

5-2021

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Pierre Clare

Committee Members

Eric Swartz

Daniel Cristol

Abstract

The tensor product of two finite irreducible representations of sl(2,C) decomposes in the classical Clebsch-Gordan formula. In "Poisson and Fourier Transforms for Tensor Products," explicit intertwiners for the classical Clebsch-Gordan formula, known as Poisson and Fourier transforms, were introduced. When q is not a root of unity, the representation theory of the quantum group Uq(sl(2,C)) is analogous to that of sl(2,C) and finite irreducible representations decompose in the quantum Clebsch-Gordan formula. We introduce an algebraic approach to constructing an explicit holographic transform which is an intertwiner for the classical Clebsch-Gordan formula. We show this transform coincides with the Poisson transform up to a constant factor, which we compute. We then employ the same algebraic method to determine a holographic transform in the quantum case. Finally, we provide a conjectural form of a q-analogue to the Poisson transform and prove the form is correct in at least one special case.

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