R-groups and geometric structure in the representation theory of SL(N)

Jamila Jawdat; Roger Plymen

doi:10.4171/JNCG/55

R-groups and geometric structure in the representation theory of SL(N)

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Abstract

Let F be a nonarchimedean local field of characteristic zero and let G = D SL(N) = SL(N, F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the K-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the R-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in [2]. © European Mathematical Society.

Original language	English
Pages (from-to)	265-279
Number of pages	14
Journal	Journal of Noncommutative Geometry
Volume	4
Issue number	2
DOIs	https://doi.org/10.4171/JNCG/55
Publication status	Published - 2010

Keywords

Elliptic representations
K-theory
L-packets
Local field
Reduced C*-algebra
Special linear group

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10.4171/JNCG/55

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title = "R-groups and geometric structure in the representation theory of SL(N)",

abstract = "Let F be a nonarchimedean local field of characteristic zero and let G = D SL(N) = SL(N, F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the K-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the R-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in [2]. {\textcopyright} European Mathematical Society.",

keywords = "Elliptic representations, K-theory, L-packets, Local field, Reduced C*-algebra, Special linear group",

author = "Jamila Jawdat and Roger Plymen",

year = "2010",

doi = "10.4171/JNCG/55",

language = "English",

volume = "4",

pages = "265--279",

journal = "Journal of Noncommutative Geometry",

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publisher = "European Mathematical Society",

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T1 - R-groups and geometric structure in the representation theory of SL(N)

AU - Jawdat, Jamila

AU - Plymen, Roger

PY - 2010

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N2 - Let F be a nonarchimedean local field of characteristic zero and let G = D SL(N) = SL(N, F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the K-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the R-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in [2]. © European Mathematical Society.

AB - Let F be a nonarchimedean local field of characteristic zero and let G = D SL(N) = SL(N, F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the K-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the R-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in [2]. © European Mathematical Society.

KW - Elliptic representations

KW - K-theory

KW - L-packets

KW - Local field

KW - Reduced C-algebra

KW - Special linear group

U2 - 10.4171/JNCG/55

DO - 10.4171/JNCG/55

M3 - Article

SN - 1661-6952

VL - 4

SP - 265

EP - 279

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 2

ER -

R-groups and geometric structure in the representation theory of SL(N)

Abstract

Keywords

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