Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-29T07:29:58.605Z Has data issue: false hasContentIssue false
  • English
  • Français

GEOMETRIC STRUCTURE IN THE TEMPERED DUAL OF SLℓ(F): TORAL CASE

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  01 August 2011

KUOK FAI CHAO
KUOK FAI CHAO*
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Taiwan (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the tempered representations derived from the principal series of SLℓ(F) and their geometric structure. In particular, we give the parameterization for special representations and prove the tempered part of the Aubert–Baum–Plymen conjecture for the toral cases of SLℓ(F).

Keywords

special linear grouptemperedp-adicrepresentations

MSC classification

Secondary: 20G05: Representation theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 425 - 432
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Aubert, A.-M., Baum, P. and Plymen, R. J., The Hecke Algebra of a Reductive p-adic Group: A Geometric Conjecture, Aspects of Mathematics, 37 (Vieweg, Braunschweig, 2006), pp. 1–34.Google Scholar
[2]Aubert, A.-M., Baum, P. and Plymen, R. J., ‘Geometric structure in the representation theory of p-adic groups’, C. R. Acad. Sci. Paris, Ser. I 345 (2007), 573–578.CrossRefGoogle Scholar
[3]Aubert, A.-M., Baum, P. and Plymen, R. J., ‘Geometric structure in the principal series of the p-adic group G 2’, Represent. Theory 15 (2011), 126–169.CrossRefGoogle Scholar
[4]Baum, P. and Connes, A., ‘Chern character for discrete groups’, in: A Fête of Topology (Academic Press, Boston, 1988), pp. 163–232.CrossRefGoogle Scholar
[5]Bernstein, J., ‘Representation of p-adic groups’, Notes by K. E. Rumelhart, Harvard University, 1992.Google Scholar
[6]Bernstein, J. and Zelevinsky, A., ‘Induced representations of reductive p-adic groups I’, Ann. Sci. Éc. Norm. Supér. (4) 10(4) (1977), 441–472.CrossRefGoogle Scholar
[7]Gelbart, S. and Knapp, A., ‘Irreducible constituents of principal series of SLn(k)’, Duke Math. J. 48 (1981), 313–326.CrossRefGoogle Scholar
[8]Gelbart, S. and Knapp, A., ‘L-indistinguishability and R-groups for the special linear group’, Adv. Math. 43(2) (1982), 101–121.CrossRefGoogle Scholar
[9]Gel’fand, I. M., Graev, M. I. and Pyatetskii-Shapiro, I. I., Representation Theory and Automorphic Functions (Saunders, Philadephia, 1969).Google Scholar
[10]Goldberg, D., ‘R-groups and elliptic representations for SLn’, Pacific J. Math. 165 (1994), 77–92.CrossRefGoogle Scholar
[11]Jawdat, J. and Plymen, R. J., ‘R-groups and geometric structure in the representation theory of SL(N)’, J. Noncommut. Geom. 4 (2010), 265–279.CrossRefGoogle Scholar
[12]Keys, D., ‘On the decomposition of reducible principal series representations of p-adic Chevalley groups’, Pacific J. Math. 101 (1982), 351–388.CrossRefGoogle Scholar
[13]Zelevinsky, A., ‘Induced representation of reductive p-adic groups II’, Ann. Sci. Éc. Norm. Supér. 13(4) (1980), 165–210.CrossRefGoogle Scholar