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

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Structure of the degenerate principal series on symmetric R-spaces and small representations. / Möllers, Jan; Schwarz, Benjamin.

I: Journal of Functional Analysis, Bind 266, Nr. 6, 2014, s. 3508–3542.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Möllers, Jan ; Schwarz, Benjamin. / Structure of the degenerate principal series on symmetric R-spaces and small representations. I: Journal of Functional Analysis. 2014 ; Bind 266, Nr. 6. s. 3508–3542.

Bibtex

@article{98323288a3f840b5864e2ccf6b09231a,
title = "Structure of the degenerate principal series on symmetric R-spaces and small representations",
abstract = "Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whosenilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We studythe degenerate principal series representations of $G$ on $C^\infty(X)$ in thecase where $P$ is not conjugate to its opposite parabolic. We find the pointsof reducibility, the composition series and all unitarizable constituents.Among the unitarizable constituents we identify some small representationshaving as associated variety the minimal nilpotent $K_{\mathbb{C}}$-orbit in$\mathfrak{p}_{\mathbb{C}}^*$, where $K_{\mathbb{C}}$ is the complexificationof a maximal compact subgroup $K\subseteq G$ and$\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartandecomposition.",
author = "Jan M{\"o}llers and Benjamin Schwarz",
year = "2014",
doi = "10.1016/j.jfa.2014.01.006",
language = "English",
volume = "266",
pages = "3508–3542",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "6",

}

RIS

TY - JOUR

T1 - Structure of the degenerate principal series on symmetric R-spaces and small representations

AU - Möllers, Jan

AU - Schwarz, Benjamin

PY - 2014

Y1 - 2014

N2 - Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whosenilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We studythe degenerate principal series representations of $G$ on $C^\infty(X)$ in thecase where $P$ is not conjugate to its opposite parabolic. We find the pointsof reducibility, the composition series and all unitarizable constituents.Among the unitarizable constituents we identify some small representationshaving as associated variety the minimal nilpotent $K_{\mathbb{C}}$-orbit in$\mathfrak{p}_{\mathbb{C}}^*$, where $K_{\mathbb{C}}$ is the complexificationof a maximal compact subgroup $K\subseteq G$ and$\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartandecomposition.

AB - Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whosenilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We studythe degenerate principal series representations of $G$ on $C^\infty(X)$ in thecase where $P$ is not conjugate to its opposite parabolic. We find the pointsof reducibility, the composition series and all unitarizable constituents.Among the unitarizable constituents we identify some small representationshaving as associated variety the minimal nilpotent $K_{\mathbb{C}}$-orbit in$\mathfrak{p}_{\mathbb{C}}^*$, where $K_{\mathbb{C}}$ is the complexificationof a maximal compact subgroup $K\subseteq G$ and$\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartandecomposition.

U2 - 10.1016/j.jfa.2014.01.006

DO - 10.1016/j.jfa.2014.01.006

M3 - Journal article

VL - 266

SP - 3508

EP - 3542

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 6

ER -