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On Irreducible Representations of So2n+1 × So2m

Published online by Cambridge University Press:  20 November 2018

Benedict H. Gross
Affiliation:
Department of Mathematics, Harvard University Cambridge, Massachussets 02138 USA, e-mail: [email protected]
Dipendra Prasad
Affiliation:
Mehta Research Institute, 10 Kasturba Gandhi Marg Allahabad 211012, India, e-mail: [email protected]
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Abstract

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In this paper, we study the restriction of irreducible representations of the group SO2n+1 × SO2m to a spherical subgroup.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

[Bl] Borel, A., Linear algebraic groups, Springer, Graduate Texts in Math. 126, 1991.Google Scholar
[B2] Borel, A., Automorphic L-functions. In: Automorphic forms, representations, and L-functions, Proc. Sympos. Pure Math. 33, Amer. Math. Soc. (1979), 2762.Google Scholar
[BZ] Bernstein, J. and Zelevinsky, A., Representations of the group GL(n,F) where Fis a non-Archimedean local field, Uspekhi. Nat. Nauk. 31(1976), 570.Google Scholar
[Br] Brion, M., Classification des espaces homogènes sphériques, Compositio Math. 63(1987), 189208.Google Scholar
[C] Casselman, W., Canonical extensions of Harish-Chandra modules to representations of G, Canad. J. Math. 41(1989), 385438.Google Scholar
[F-Z] Feit, W. and Zuckermann, G., Reality properties of conjugacy classes in spin groups and symplectic groups, Contemp. Math. 13(1982), 239253.Google Scholar
[G-PS-R] Ginzburg, D., Piatetski-Shapiro, I. and Rallis, S., Rankin-Selberg integrals for GL × SO(V), to appear.Google Scholar
[G] Gross, B. H., L-functions at the central critical point. In: Motives, Proc. Sympos. Pure Math., Amer. Math. Soc, (1)55(1994)527536.Google Scholar
[G-P] Gross, B. H. and Prasad, D., On the decomposition of a representation of SOn when restricted to SOn−1 , Canad. J. Math. 44(1992), 9741002.Google Scholar
[K] Keys, D., L-indistinguishability and R-groups for quasi-split groups: Unitary groups of even dimension, Ann. Sci. ácole Norm. Sup. 20(1987), 3164.Google Scholar
[K-Sh] Keys, D. and Shahidi, F., Artin L-functions and normalisation of intertwining operators, Ann. Sci. ácole Norm. Sup. 21(1988), 6789.Google Scholar
[MH] Milnor, J. and Husemoller, D., Symmetric bilinear forms, Ergeb. Bond 73, Springer-Verlag, 1973.Google Scholar
[MVW] Moeglin, C., Vigneras, M.-F. and Waldspurger, J. L., Correspondence de Howe sur un corps p-adique, Lecture Notes in Math. 1291, Springer-Verlag, 1987.Google Scholar
[PI] Prasad, D., Trilinear forms for representations of GL(2) and local epsilon factors, Compositio Math. 75(1990), 146.Google Scholar
[P2] Prasad, D., Invariant linear forms for representations of GL(2), Amer. J. Math. 114(1992), 13171363.Google Scholar
[Ro1] Rodier, F., Modèles de Whittaker des réprésentations admissibles des groupes reductives p-adiques quasideployes, unpublished.Google Scholar
[Ro2] Rodier, F., Sur les facteurs Euleriens associés aux sous-quotients des séries principales des groupes reductifs p-adiques, Journées Automorphes, Publications Mathématiques de l'université Paris VII15, 1983.Google Scholar
[Sa] Saito, H., On Tunnell's theorem on characters GL(2), Compositio Math. 85(1993), 99108.Google Scholar
[S1] Serre, J.-P., A course in arithmetic, Springer, Graduate Texts in Math. 7, 1973.Google Scholar
[S2] Serre, J.-P., Cohomologie Galoisienne, Springer, Lecture Notes in Math. 5, 1973.Google Scholar
[S3] Serre, J.-P., Résumé des cours de l'année 1990-1991, Collège de France.Google Scholar
[Sh] Shahidi, F., Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J. 66(1992), 141.Google Scholar
[Sol] Soudry, D., Rankin-SeIberg convolution for So2l+1 × GLn: Local theory, Memoirs Amer. Math. Soc, 500(1993).Google Scholar
[So2] Soudry, D., On the Archimedean theory of Rankin-Selberg convolution for So2l+1 × GLn , to appear.Google Scholar
[Sp] Springer, T., On the equivalence of quadratic forms, Proc. Kon. Nederl. Akad. Wetensch. (A) 62(1959), 241253.Google Scholar
[SS] Springer, T. and Steinberg, R., Conjugacy Classes, In: Seminar on Algebraic groups and related finite groups, Springer, Lecture Notes in Math. 131, 1970, 167266.Google Scholar
[St] Steinberg, R., Lectures on Chevalley Groups, Yale University Press, 1967.Google Scholar
[T] Tate, J., Number theoretic background. In: Automorphic forms, representations, and L-functions, Proc. Sympos. Pure Math. (2) 33, Amer. Math. Soc, 1979, 326.Google Scholar
[Tu] Tunnell, J., Local epsilon factors and characters of GL(2), Amer J. Math. 105(1983), 12771308.Google Scholar
[V] Vogan, D., The local Langlands conjecture, Contemp. Math. 145(1993), 305379.Google Scholar
[W] Wallach, N., Real reductive groups I and II, Academic Press, 1992.Google Scholar
[Ze] Zelevinsky, A., Induced representations of reductive p-adic groups II, Ann. Sci. ácole Norm. Sup. 13 (1980), 165210.Google Scholar