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Semisimple characters for \(p\)-adic classical groups. (English) Zbl 1063.22018

From the introduction: Let \(\overline{G}=GL(n,F)\), where \(F\) denotes a \(p\)-adic field with \(p>2\), and let \(G\) be a classical group realized as the fixed-point subgroup for an involution on \(\overline{G}\). The author, extending his earlier work [Proc. Lond. Math. Soc., III. Ser. 83, 120–140 (2001; Zbl 1017.22012)] as well as work of C. J. Bushnell and P. C. Kutzko [Compos. Math. 119, 53–97 (1999; Zbl 0933.22027)], defines a semisimple character for \(G\) and for \(\overline{G}\) and establishes certain functorial properties. Finally, he shows that any supercuspidal representation of \(G\) contains such a semisimple character.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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[1] L. Blasco, Description du dual admissible de \(U(2,1)(F)\) par la théorie des types de C. Bushnell et P. Kutzko , Manuscripta Math. 107 (2002), 151–186. · Zbl 1108.22011 · doi:10.1007/s002290100231
[2] P. Broussous and B. Lemaire, Building of \(\GL(m,D)\) and centralizers , Transform. Groups 7 (2002), 15–50. · Zbl 1001.22016 · doi:10.1007/BF01253463
[3] P. Broussous and S. Stevens, Buildings of classical groups and centralizers of Lie algebra elements , · Zbl 1165.22018
[4] C. J. Bushnell and G. Henniart, Local tame lifting for \(\GL(N)\), I: Simple characters , Inst. Hautes Études Sci. Publ. Math. 83 (1996), 105–233. · Zbl 0878.11042 · doi:10.1007/BF02698646
[5] ——–, Local Tame Lifting for \(\GL(N)\), II: Wildly Ramified Supercuspidals , Astérisque 254 , Soc. Math. France, Montrouge, 1999. · Zbl 0920.11079
[6] C. J. Bushnell and P. C. Kutzko, The Admissible Dual of \(\GL(N)\) via Compact Open Subgroups , Princeton Univ. Press, Princeton, 1993. · Zbl 0787.22016
[7] –. –. –. –., Smooth representations of reductive \(p\)-adic groups: Structure theory via types , Proc. London Math. Soc. (3) 77 (1998), 582–634. · Zbl 0911.22014 · doi:10.1112/S0024611598000574
[8] –. –. –. –., Semisimple types in \(\GL_n\) , Compositio Math. 119 (1999), 53–97. · Zbl 0933.22027 · doi:10.1023/A:1001773929735
[9] G. Glauberman, Correspondences of characters for relatively prime operator groups , Canad. J. Math. 20 (1968), 1465–1488. · Zbl 0167.02602 · doi:10.4153/CJM-1968-148-x
[10] V. Sécherre, Représentations lisses de \(\GL(m,D)\), I: Caractères simples , Bull. Soc. Math. France 132 (2004), 327–396. · Zbl 1079.22016
[11] S. Stevens, Double coset decompositions and intertwining , Manuscripta Math. 106 (2001), 349–364. · Zbl 0988.22008 · doi:10.1007/PL00005887
[12] –. –. –. –., Intertwining and supercuspidal types for \(p\)-adic classical groups , Proc. London Math. Soc. (3) 83 (2001), 120–140. · Zbl 1017.22012 · doi:10.1112/plms/83.1.120
[13] –. –. –. –., Semisimple strata for \(p\)-adic classical groups , Ann. Sci. École Norm. Sup. (4) 35 (2002), 423–435. · Zbl 1009.22017 · doi:10.1016/S0012-9593(02)01095-9
[14] ——–, Types and supercuspidal representations of \(p\)-adic symplectic groups , Ph.D. dissertation, King’s College, London, 1998, http://www.mth.uea.ac.uk/ h008/research.html J.-K. Yu, Construction of tame supercuspidal representations , J. Amer. Math. Soc. 14 (2001), 579–622. JSTOR: · Zbl 0971.22012 · doi:10.1090/S0894-0347-01-00363-0
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