Equivalence theorems and an explicit formula for the biquantization character

TL;DR

This paper establishes a connection between biquantization characters in reduction algebras and Penney eigendistributions in harmonic analysis on Lie groups, providing explicit formulas and theoretical insights.

Contribution

It proves that the biquantization character equals the Penney eigendistribution character, offering a new explicit formula and theoretical link in the context of Lie groups and reduction algebras.

Findings

Biquantization character equals Penney eigendistribution character

Provides an explicit formula for the biquantization character

Links biquantization with harmonic analysis on Lie groups

Abstract

We prove that the biquantization character of Cattaneo-Torossian for the reduction algebra is the character of the Penney eigendistribution from harmonic analysis on Lie groups. Part of the author's PhD thesis at University Paris 7, 2009.