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Structure of the degenerate principal series on symmetric R-spaces and small representations

Möllers J, Schwarz B (2014)

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Publication Type: Journal article

Publication year: 2014

Journal

Publisher: Elsevier

Book Volume: 266

Pages Range: 3508–3542

Journal Issue: 6

DOI: 10.1016/j.jfa.2014.01.006

Abstract

Let G be a simple real Lie group with maximal parabolic subgroup P   whose nilradical is abelian. Then X=G/P$X=G/P$ is called a symmetric R-space. We study the degenerate principal series representations of G   on C^∞(X)$C^{\infty }(X)$ in the case where P   is not conjugate to its opposite parabolic. We find the points of reducibility, the composition series and all unitarizable constituents. Among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent K_C$K_{\mathbb{C}}$-orbit in ${\mathfrak{p}}_{\mathbb{C}}^{⁎}$, where K_C$K_{\mathbb{C}}$ is the complexification of a maximal compact subgroup K⊆G$K\subseteq G$ and g=k+p$\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartan decomposition.

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APA:

Möllers, J., & Schwarz, B. (2014). Structure of the degenerate principal series on symmetric R-spaces and small representations. Journal of Functional Analysis, 266(6), 3508–3542. https://dx.doi.org/10.1016/j.jfa.2014.01.006

MLA:

Möllers, Jan, and Benjamin Schwarz. "Structure of the degenerate principal series on symmetric R-spaces and small representations." Journal of Functional Analysis 266.6 (2014): 3508–3542.

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