Date of Award:

12-2026

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Peter Crooks

Committee

Peter Crooks

Committee

Matthew Young

Committee

David Brown

Abstract

Let G be a complex semisimple linear algebraic group with 𝐶 a conjugacy class of parabolic subgroups of G. In previous work, Dr. Crooks defines 𝑢𝐶→ B𝐶 , a universal flat family of a fine Hamiltonian Lagrangian G-bundles over 𝐶, and shows that 𝑢𝐶 is a family of regular Poisson varieties. This manuscript introduces a natural candidate for a quasi-Poisson analog of Dr. Crooks’s construction, 𝑢𝐶, using the framework of quasi-Poisson geometry established by Alekseev, Kosmann-Scwarzbach, and Meinrenken. It will be shown that this proposed quasi-Poisson analog indeed has a valid quasi-Poisson structure and is a family of regular quasi-Poisson varieties.

Included in

Mathematics Commons

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