Abstract: Let $G$ be a real reductive Lie group (such as $\text{GL}(n,\mathbb{R})$, $\text{SO}(n,\mathbb{R})$ or $\text{Sp}(2n,\mathbb{R}))$. The problem of classifying all irreducible, unitary representations of $G$ has deep connections with quantum mechanics, yet it remains unsolved for nearly a century. In this talk, we will recall some known results in the classification problem, and will explore how the `atlas' software can be used to verify and give insights on proving various conjectures related to the problem.
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