The Plancherel Formula, the Plancherel Theorem, and the Fourier transform of orbital integrals
We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.
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arXiv subjects
Rebecca A. Herb
Publications and source records attributed to Rebecca A. Herb.
Some results on the admissible representations of non-connected reductive p-adic groups
We examine the theory of induced representations for non-connected reductive $p$-adic groups for which $G/G^0$ is abelian. We first examine the structure of those representations of the form $\Ind_{P^0}^G(σ),$ where $P^0$ is a parabolic subgroup of $G^0$ and $\s$ is a discrete series representation of the Levi component of $P^0.$ Here we develop a theory of $R$--groups, extending the theory in the connected case. We then prove some general results in the theory of representations of non-connected $p$-adic groups whose component group is abelian. We define the notion of cuspidal parabolic for $G$ in order to give a context for this discussion. Intertwining operators for the non-connected case are examined and the notions of supercuspidal and discrete series are defined. Finally, we examine parabolic induction from a cuspidal parabolic subgroup of $G.$ Here we also develop a theory of $R$--groups, and show that these groups parameterize the induced representations in a manner that is consistent with the connected case and with the first set of results as well.
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