Raising nilpotent orbits in wave-front sets
HTML articles powered by AMS MathViewer
- by Dihua Jiang, Baiying Liu and Gordan Savin
- Represent. Theory 20 (2016), 419-450
- DOI: https://doi.org/10.1090/ert/490
- Published electronically: October 26, 2016
- PDF | Request permission
Abstract:
We study wave-front sets of representations of reductive groups over global or non-archimedean local fields.References
- Rolf Berndt and Ralf Schmidt, Elements of the representation theory of the Jacobi group, Progress in Mathematics, vol. 163, Birkhäuser Verlag, Basel, 1998. MR 1634977, DOI 10.1007/978-3-0348-0283-3
- Roger W. Carter, Finite groups of Lie type, Wiley Classics Library, John Wiley & Sons, Ltd., Chichester, 1993. Conjugacy classes and complex characters; Reprint of the 1985 original; A Wiley-Interscience Publication. MR 1266626
- David H. Collingwood and William M. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Mathematics Series, Van Nostrand Reinhold Co., New York, 1993. MR 1251060
- E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Mat. Sbornik N.S. 30(72) (1952), 349–462 (3 plates) (Russian). MR 0047629
- David Ginzburg, Certain conjectures relating unipotent orbits to automorphic representations, Israel J. Math. 151 (2006), 323–355. MR 2214128, DOI 10.1007/BF02777366
- D. Ginzburg, S. Rallis, and D. Soudry, On Fourier coefficients of automorphic forms of symplectic groups, Manuscripta Math. 111 (2003), no. 1, 1–16. MR 1981592, DOI 10.1007/s00229-003-0355-7
- Steven Glenn Jackson and Alfred G. Noël, Prehomogeneous spaces associated with complex nilpotent orbits, J. Algebra 289 (2005), no. 2, 515–557. MR 2142384, DOI 10.1016/j.jalgebra.2005.02.017
- Dihua Jiang and Baiying Liu, On special unipotent orbits and Fourier coefficients for automorphic forms on symplectic groups, J. Number Theory 146 (2015), 343–389. MR 3267118, DOI 10.1016/j.jnt.2014.03.002
- Hung Yean Loke and Gordan Savin, On minimal representations of Chevalley groups of type $D_n,\ E_n$ and $G_2$, Math. Ann. 340 (2008), no. 1, 195–208. MR 2349773, DOI 10.1007/s00208-007-0144-9
- C. Mœglin, Front d’onde des représentations des groupes classiques $p$-adiques, Amer. J. Math. 118 (1996), no. 6, 1313–1346 (French, with French summary). MR 1420926, DOI 10.1353/ajm.1996.0051
- C. Mœglin and J.-L. Waldspurger, Modèles de Whittaker dégénérés pour des groupes $p$-adiques, Math. Z. 196 (1987), no. 3, 427–452 (French). MR 913667, DOI 10.1007/BF01200363
- C. Mœglin and J.-L. Waldspurger, Spectral decomposition and Eisenstein series, Cambridge Tracts in Mathematics, vol. 113, Cambridge University Press, Cambridge, 1995. Une paraphrase de l’Écriture [A paraphrase of Scripture]. MR 1361168, DOI 10.1017/CBO9780511470905
- Monica Nevins, Admissible nilpotent orbits of real and $p$-adic split exceptional groups, Represent. Theory 6 (2002), 160–189. MR 1915090, DOI 10.1090/S1088-4165-02-00134-6
- Sandeep Varma, On a result of Moeglin and Waldspurger in residual characteristic 2, Math. Z. 277 (2014), no. 3-4, 1027–1048. MR 3229979, DOI 10.1007/s00209-014-1292-8
- Jean-Loup Waldspurger, Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque 269 (2001), vi+449 (French, with English and French summaries). MR 1817880
- Martin H. Weissman, The Fourier-Jacobi map and small representations, Represent. Theory 7 (2003), 275–299. MR 1993361, DOI 10.1090/S1088-4165-03-00197-3
Bibliographic Information
- Dihua Jiang
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 260974
- Email: dhjiang@math.umn.edu
- Baiying Liu
- Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
- MR Author ID: 953254
- Email: liu2053@purdue.edu
- Gordan Savin
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 250304
- Email: savin@math.utah.edu
- Received by editor(s): May 4, 2016
- Received by editor(s) in revised form: October 6, 2016
- Published electronically: October 26, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Represent. Theory 20 (2016), 419-450
- MSC (2010): Primary 11F70, 22E50; Secondary 11F85, 22E55
- DOI: https://doi.org/10.1090/ert/490
- MathSciNet review: 3564676