Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-21T16:10:18.735Z Has data issue: false hasContentIssue false
  • English
  • Français

Extensions of representations of p-adic groups

Published online by Cambridge University Press:  11 January 2016

Jeffrey D. Adler  and
Dipendra Prasad
Jeffrey D. Adler
Affiliation:
American University, Washington, DC 20016-8050, USA, jadler@american.edu
Dipendra Prasad
Affiliation:
Tata Institute of Fundamental Research, Mumbai 400 005, India, dprasad@math.tifr.res.in
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 calculate extensions between certain irreducible admissible representations of p-adic groups.

Keywords

11F7022E55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 208: Memorial Volume for Professor Hiroshi Saito , December 2012 , pp. 171 - 199
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

References

[1] Arthur, J., On elliptic tempered characters, Acta Math. 171 (1993), 73–138.Google Scholar
[2] Bernšteĭn, I. N. and Zelevinskiĭ, A. V., Induced representations of reductive p-adic groups, I, Ann. Sci. Ec. Norm. Supér. (4) 10 (1977), 441–472.CrossRefGoogle Scholar
[3] Bushnell, C. J. and Kutzko, P. C., Smooth representations of reductive p-adic groups: Structure theory via types, Proc. Lond. Math. Soc. (3) 77 (1998), 582–634.CrossRefGoogle Scholar
[4] Casselman, W., A new nonunitarity argument for p-adic representations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 907–928.Google Scholar
[5] Casselman, W., Introduction to the theory of admissible representations of p-adic reductive groups, preprint, 1995.Google Scholar
[6] Dat, J.-F., Espaces symétriques de Drinfeld et correspondence de Langlands locale, Ann. Sci. Éc. Norm. Supér. (4) 39 (2006), 1–74.Google Scholar
[7] Goldberg, D. and Roche, A., Types in SLn , Proc. Lond. Math. Soc. (3) 85 (2002), 119–138.Google Scholar
[8] Goldberg, D. and Roche, A., Hecke algebras and SLn-types, Proc. Lond. Math. Soc. (3) 90 (2005), 87–131.Google Scholar
[9] Haines, T. J., Kottwitz, R. E., and Prasad, A., Iwahori-Hecke algebras, J. Ramanujan Math. Soc. 25 (2010), 113–145.Google Scholar
[10] Howe, R. and Tan, E.-C., Nonabelian Harmonic Analysis: Applications of SL(2,R), Universitext, Springer, New York, 1992.Google Scholar
[11] Kazhdan, D., Cuspidal geometry of p-adic groups, J. Anal. Math. 47 (1986), 1–36.Google Scholar
[12] Kim, J.-L., Supercuspidal representations: An exhaustion theorem, J. Amer. Math. Soc. 20 (2007), 273–320.CrossRefGoogle Scholar
[13] Morris, L., Tamely ramified intertwining algebras, Invent. Math. 114 (1993), 1–54.Google Scholar
[14] Morris, L., Level zero G-types, Compos. Math. 118 (1999), 135–157.Google Scholar
[15] Moy, A. and Prasad, G., Jacquet functors and unrefined minimal K-types, Comment. Math. Helv. 71 (1996), 98–121.CrossRefGoogle Scholar
[16] Opdam, E. and Solleveld, M., Extensions of tempered representations, preprint, arXiv:1105.3802v2 [math.RT]Google Scholar
[17] Orlik, S., On extensions of generalized Steinberg representations, J. Algebra 293 (2005), 611–630.Google Scholar
[18] Prasad, D. and Takloo-Bighash, R., Bessel models for GSp(4), J. Reine Angew. Math. 655 (2011), 189–243.Google Scholar
[19] Savin, G., A tale of two Hecke algebras, preprint, arXiv:1202.1486v1 [math.RT]Google Scholar
[20] Schneider, P. and Stuhler, U., Representation theory and sheaves on the Bruhat-Tits building, Publ. Math. Inst. Hautes Etudes Sci. 85 (1997), 97–191.Google Scholar
[21] Serre, J.-P., Local Fields, Grad. Texts in Math. 67, Springer, New York, 1979.Google Scholar
[22] Stevens, S., The supercuspidal representations of p-adic classical groups, Invent. Math. 172 (2008), 289–352.Google Scholar
[23] Vignéras, M.-F., Extensions between irreducible representations of a p-adic GL(n), Pacific J. Math. 181 (1997), 349–357.Google Scholar
[24] Yu, J.-K., Construction of tame supercuspidal representations, J. Amer. Math. Soc. 14 (2001), 579–622.Google Scholar