×

zbMATH — the first resource for mathematics

The unitary spherical spectrum for split classical groups. (English) Zbl 1188.22010
The paper completes the classification of the spherical unitary dual for the symplectic and split orthogonal groups over local fields using affine Hecke algebras. Most of the results were known earlier [cf., e.g., D. Barbasch and D. Ciubotaru, Compos. Math. 145, No. 6, 1563–1616 (2009; Zbl 1183.22008)]. A new result is necessary conditions for unitarity in the real case.

MSC:
22E46 Semisimple Lie groups and their representations
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] DOI: 10.1007/BF01388842 · Zbl 0676.22012 · doi:10.1007/BF01388842
[2] DOI: 10.2307/2152779 · Zbl 0835.22016 · doi:10.2307/2152779
[3] Barbasch, Pure Appl. Math. Q. 1 pp 755– (2005) · Zbl 1133.22301 · doi:10.4310/PAMQ.2005.v1.n4.a3
[4] DOI: 10.1090/S0002-9939-99-04482-2 · Zbl 0905.22008 · doi:10.1090/S0002-9939-99-04482-2
[5] Barbasch, Functional analysis 8 (2004)
[6] Zelevinsky, Annales Scient. Éc. Norm. Sup. 13 pp 165– (1980)
[7] Barbasch, Proc. Symp. Pure Math. 68 pp 97– (2000) · doi:10.1090/pspum/068/1767894
[8] Weyl, Princeton Landmarks in Mathematics (1997)
[9] Barbasch, Geometry and representation theory of real and p-adic groups pp 1– (1996)
[10] Barbasch, Proc. of International Congress of Mathematicians, Kyoto, 1990 pp 769– (1990)
[11] Vogan, Harmonic analysis on reductive groups pp 315– (1991) · doi:10.1007/978-1-4612-0455-8_17
[12] DOI: 10.1007/BF01393972 · Zbl 0692.22006 · doi:10.1007/BF01393972
[13] DOI: 10.1007/BF01394418 · Zbl 0598.22008 · doi:10.1007/BF01394418
[14] Adams, The Langlands classification and irreducible characters of real reductive groups 104 (1992) · Zbl 0756.22004 · doi:10.1007/978-1-4612-0383-4
[15] DOI: 10.1215/S0012-7094-82-04946-8 · Zbl 0536.22022 · doi:10.1215/S0012-7094-82-04946-8
[16] Vogan, Progress in Mathematics 15 (1981)
[17] DOI: 10.1016/j.jalgebra.2003.07.026 · Zbl 1103.22004 · doi:10.1016/j.jalgebra.2003.07.026
[18] Tadic, Annales Scient. Éc. Norm. Sup. 19 pp 335– (1986)
[19] DOI: 10.2307/1970611 · Zbl 0188.45303 · doi:10.2307/1970611
[20] DOI: 10.2307/121129 · Zbl 0960.22009 · doi:10.2307/121129
[21] DOI: 10.1016/j.aim.2006.03.004 · Zbl 1154.22019 · doi:10.1016/j.aim.2006.03.004
[22] DOI: 10.1353/ajm.1998.0003 · Zbl 0965.22016 · doi:10.1353/ajm.1998.0003
[23] DOI: 10.1112/jlms/s2-19.1.41 · Zbl 0407.20035 · doi:10.1112/jlms/s2-19.1.41
[24] Lusztig, Annals of Mathematics Studies 107 (1984)
[25] Knapp, Cohomological induction and unitary representations 45 (1995) · Zbl 0863.22011
[26] Knapp, Representation theory of real semisimple groups: an overview based on examples (1986) · Zbl 0604.22001
[27] Collingwood, Nilpotent orbits in semisimple Lie algebras (1993) · Zbl 0972.17008
[28] Chang, Compositio Math. 88 pp 265– (1993)
[29] Cartier, Automorphic forms and L-functions 33 pp 111– (1979)
[30] DOI: 10.1007/BF01390139 · Zbl 0334.22012 · doi:10.1007/BF01390139
[31] DOI: 10.1090/S1088-4165-08-00311-7 · Zbl 1186.22017 · doi:10.1090/S1088-4165-08-00311-7
[32] DOI: 10.2307/1971193 · Zbl 0582.22007 · doi:10.2307/1971193
[33] Barbasch, Representation Theory of Reductive Groups, Park City, UT, 1982 40 pp 21– (1983)
[34] DOI: 10.1016/0022-1236(80)90026-9 · Zbl 0436.22011 · doi:10.1016/0022-1236(80)90026-9
[35] DOI: 10.1090/S0002-9939-98-04090-8 · Zbl 0896.22004 · doi:10.1090/S0002-9939-98-04090-8
[36] DOI: 10.1007/BF00116514 · Zbl 0862.22015 · doi:10.1007/BF00116514
[37] Barbasch, Compositio Math.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.