Restrictions of representations of classical groups: examples
Sur les Conjectures de Gross et Prasad. I, Astérisque, no. 346 (2012), pp. 111-170.
@incollection{AST_2012__346__111_0,
     author = {Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra},
     title = {Restrictions of representations of classical groups: examples},
     booktitle = {Sur les Conjectures de Gross et Prasad. I},
     editor = {Gan, W. T. and Gross, B. H. and Prasad, D. and Waldspurger, J.-L.},
     series = {Ast\'erisque},
     pages = {111--170},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {346},
     year = {2012},
     mrnumber = {3202557},
     zbl = {1279.22023},
     language = {en},
     url = {http://www.numdam.org/item/AST_2012__346__111_0/}
}
TY  - CHAP
AU  - Gan, Wee Teck
AU  - Gross, Benedict H.
AU  - Prasad, Dipendra
TI  - Restrictions of representations of classical groups: examples
BT  - Sur les Conjectures de Gross et Prasad. I
AU  - Collectif
ED  - Gan, W. T.
ED  - Gross, B. H.
ED  - Prasad, D.
ED  - Waldspurger, J.-L.
T3  - Astérisque
PY  - 2012
SP  - 111
EP  - 170
IS  - 346
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2012__346__111_0/
LA  - en
ID  - AST_2012__346__111_0
ER  - 
%0 Book Section
%A Gan, Wee Teck
%A Gross, Benedict H.
%A Prasad, Dipendra
%T Restrictions of representations of classical groups: examples
%B Sur les Conjectures de Gross et Prasad. I
%A Collectif
%E Gan, W. T.
%E Gross, B. H.
%E Prasad, D.
%E Waldspurger, J.-L.
%S Astérisque
%D 2012
%P 111-170
%N 346
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2012__346__111_0/
%G en
%F AST_2012__346__111_0
Gan, Wee Teck; Gross, Benedict H.; Prasad, Dipendra. Restrictions of representations of classical groups: examples, in Sur les Conjectures de Gross et Prasad. I, Astérisque, no. 346 (2012), pp. 111-170. http://www.numdam.org/item/AST_2012__346__111_0/

[1] A. Aizenbud, D. Gourevitch, S. Rallis and G. Schiffmann - "Multiplicity one theorems", Ann. of Math. 172 (2010), p. 1407-1434. | DOI | MR | Zbl

[2] I. N. Bernstein and A. V. Zelevinsky - "Induced representations of reductive 𝔭-adic groups. I", Ann. Sci. École Norm. Sup. 10 (1977), p. 441-472. | DOI | EuDML | Numdam | MR | Zbl

[3] S. Debacker and M. Reeder - "Depth-zero supercuspidal L-packets and their stability", Ann. of Math. 169 (2009), p. 795-901. | DOI | MR | Zbl

[4] S. Debacker and M. Reeder, "On some generic very cuspidal representations", Compos. Math. 146 (2010), p. 1029-1055. | DOI | MR | Zbl

[5] P. Deligne and G. Lusztig - "Representations of reductive groups over finite fields", Ann. of Math. 103 (1976), p. 103-161. | DOI | MR | Zbl

[6] A. Fröhlich and J. Queyrut - "On the functional equation of the Artin L-function for characters of real representations", Invent. Math. 20 (1973), p. 125-138. | DOI | EuDML | MR | Zbl

[7] W. T. Gan, B. H. Gross and D. Prasad - "Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups", this volume, 2012. | Numdam | MR | Zbl

[8] S. S. Gelbart and J. D. Rogawski - "L-functions and Fourier-Jacobi coefficients for the unitary group U(3)", Invent. Math. 105 (1991), p. 445-472. | DOI | EuDML | MR | Zbl

[9] S. S. Gelbart, J. D. Rogawski and D. Soudry - "Endoscopy, theta-liftings, and period integrals for the unitary group in three variables", Ann. of Math. 145 (1997), p. 419-476. | DOI | MR | Zbl

[10] D. Ginzburg, D. Jiang and S. Rallis - "On the nonvanishing of the central value of the Rankin-Selberg L-functions. II", in Automorphic representations, L-functions and applications: progress and prospects, Ohio State Univ. Math. Res. Inst. Publ., vol. 11, de Gruyter, 2005, p. 157-191. | MR | Zbl

[11] D. Ginzburg, D. Jiang and S. Rallis, "Models for certain residual representations of unitary groups", in Automorphic forms and L-functions I. Global aspects, Contemp. Math., vol. 488, Amer. Math. Soc., 2009, p. 125-146. | DOI | MR | Zbl

[12] Z. Gong and L. Grenié - "An inequality for local unitary Theta correspondence", manuscrit, 2008. | Numdam | Zbl

[13] B. H. Gross and D. Prasad - "On the decomposition of a representation of SO n when restricted to SO n-1 ", Canad. J. Math. 44 (1992), p. 974-1002. | DOI | MR | Zbl

[14] B. H. Gross and D. Prasad, "On irreducible representations of SO 2n+1 ×SO 2m ", Canad. J. Math. 46 (1994), p. 930-950. | MR | Zbl

[15] B. H. Gross and M. Reeder - "From Laplace to Langlands via representations of orthogonal groups", Bull Amer. Math. Soc. (N.S.) 43 (2006), p. 163-205. | DOI | MR | Zbl

[16] M. Harris - "L-functions of 2×2 unitary groups and factorization of periods of Hilbert modular forms", J. Amer. Math. Soc. 6 (1993), p. 637-719. | MR | Zbl

[17] M. Harris, S. S. Kudla and W. J. Sweet - "Theta dichotomy for unitary groups", J. Amer. Math. Soc. 9 (1996), p. 941-1004. | DOI | MR | Zbl

[18] M. Harris, J. S. Li and B. Y. Sun - "Theta correspondences for close unitary groups", to appear in a volume in honor of S. Kudla. | MR | Zbl

[19] K. Konno and T. Konno - "CAP automorphic representations of U E/F (4) I. Local A-packets", Kyushu Univ. Preprint Series (2003-2004).

[20] T. Konno - "Local Gross-Prasad conjecture for U(2)", slides of a talk given in Workshop on Representation theory and Automorphic Forms, National Univ. of Singapore, 2008.

[21] S. S. Kudla - "Splitting metaplectic covers of dual reductive pairs", Israel J. Math. 87 (1994), p. 361-401. | DOI | MR | Zbl

[22] J.-P. Labesse and R. P. Langlands - "L-indistinguishability for SL(2)", Canad. J. Math. 31 (1979), p. 726-785. | MR | Zbl

[23] C. Moeglin, M.-F. Vignéras and J.-L. Waldspurger - Correspondances de Howe sur un corps p-adique, Lecture Notes in Math., vol. 1291, Springer, 1987. | MR | Zbl

[24] C. Moeglin and J.-L. Waldspurger - "La conjecture locale de Gross-Prasad pour les groupes spéciaux orthogonaux: le cas général", to appear in Astérisque. | Numdam | MR | Zbl

[25] C. Moen - "The dual pair (U(3),U(1)) over a p-adic field", Pacific J. Math. 127 (1987), p. 141-154. | DOI | MR | Zbl

[26] A. Paul - "Howe correspondence for real unitary groups", J. Funct. Anal. 159 (1998), p. 384-431. | DOI | MR | Zbl

[27] D. Prasad - "Trilinear forms for representations of GL(2) and local ϵ-factors", Compositio Math. 75 (1990), p. 1-46. | EuDML | Numdam | MR | Zbl

[28] D. Prasad, "Invariant forms for representations of GL 2 over a local field", Amer. J. Math. 114 (1992), p. 1317-1363. | DOI | MR | Zbl

[29] D. Prasad, "On an extension of a theorem of Tunnell", Compositio Math. 94 (1994), p. 19-28. | EuDML | Numdam | MR | Zbl

[30] D. Prasad, "Some applications of seesaw duality to branching laws", Math. Ann. 304 (1996), p. 1-20. | DOI | EuDML | MR | Zbl

[31] D. Prasad, "Theta correspondence for unitary groups", Pacific J. Math. 194 (2000), p. 427-438. | DOI | MR | Zbl

[32] D. Prasad, "Relating invariant linear form and local epsilon factors via global methods", Duke Math. J. 138 (2007), p. 233-261. | DOI | MR | Zbl

[33] D. Prasad and R. Schulze-Pillot - "Generalised form of a conjecture of Jacquet and a local consequence", J. reine angew. Math. 616 (2008), p. 219-236. | MR | Zbl

[34] D. Prasad and R. Takloo-Bighash - "Bessel models for GSp(4)", J. reine angew. Math. 655 (2011), p. 189-243. | MR | Zbl

[35] J. D. Rogawski - Automorphic representations of unitary groups in three variables, Annals of Math. Studies, vol. 123, Princeton Univ. Press, 1990. | MR | Zbl

[36] J. D. Rogawski, "The multiplicity formula for A-packets", in The zeta functions of Picard modular surfaces, Univ. Montréal, 1992, p. 395-419. | MR | Zbl

[37] H. Saito - "On Tunnell's formula for characters of GL(2)", Compositio Math. 85 (1993), p. 99-108. | EuDML | Numdam | MR | Zbl

[38] H. Saito, "Two remarks on a theorem of Dipendra Prasad", Pacific J. Math. 234 (2008), p. 185-199. | DOI | MR | Zbl

[39] F. Sauvageot - "Principe de densité pour les groupes réductifs", Compositio Math. 108 (1997), p. 151-184. | DOI | MR | Zbl

[40] J. Tate - "Number theoretic background", in Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., 1979, p. 3-26. | MR | Zbl

[41] E. Thoma - "Die Einschränkung der Charaktere von GL(n,q) auf GL(n-1,q)", Math. Z. 119 (1971), p. 321-338. | DOI | EuDML | MR | Zbl

[42] J. B. Tunnell - "Local ϵ-factors and characters of GL(2)", Amer. J. Math. 105 (1983), p. 1277-1307. | DOI | MR | Zbl

[43] J.-L. Waldspurger - "Correspondance de Shimura", J. Math. Pures Appl. 59 (1980), p. 1-132. | MR | Zbl

[44] J.-L. Waldspurger, "Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie", Compositio Math. 54 (1985), p. 173-242. | EuDML | Numdam | MR | Zbl

[45] J.-L. Waldspurger, "Correspondances de Shimura et quaternions", Forum Math. 3 (1991), p. 219-307. | EuDML | MR | Zbl

[46] J.-L. Waldspurger, "Une formule intégrale reliée à la conjecture locale de Gross-Prasad", Compositio Mathematica 146 (2010), p. 1180-1290. | DOI | MR | Zbl

[47] J.-L. Waldspurger, "Une formule intégrale reliée à la conjecture locale de Gross-Prasad, 2e partie: extension aux représentations tempérées", this volume, 2012. | Numdam | MR | Zbl

[48] J.-L. Waldspurger, "Calcul d'une valeur d'un facteur epsilon par une formule intégrale", to appear in Astérisque. | Numdam | MR

[49] J.-L. Waldspurger, "La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux", to appear in Astérisque. | Numdam | MR | Zbl