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The Dual Pair PGL3 × G2

Published online by Cambridge University Press:  20 November 2018

Benedict H. Gross and
Gordan Savin
Benedict H. Gross
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA, USA 02138 e-mail: gross@math.harvard.edu
Gordan Savin
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT, USA 84112, e-mail: savin@math.utah.edu
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Abstract

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Let H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representation of H to the closed subgroup PGL3 × G2 .

Keywords

Primary: 22E35 and 50Secondary: 11F70

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997, pp. 376 - 384
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Aschbacher, M., The 27-dimensional module for E6. I, Invent. Math. 89 (1987), 159–196.Google Scholar
2. Borel, A., Admissible representations of semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976), 233–259.Google Scholar
3. Gross, B. H. and Prasad, D., On the decomposition of a representation of SOn when restricted to SOn−1, Can. J. Math. 44 (1992), 974–1002.Google Scholar
4. Gross, B. H. and Savin, G., Motives with Galois group G2, (1996), preprint.Google Scholar
5. Jacobson, N., Automorphisms of composition algebras, Rend. Palermo, 1958.Google Scholar
6. Lusztig, G., Some examples of square integrable representations of semisimple p-adic groups, Tran. Am. Math. Soc. 277 (1983), 623–653.Google Scholar
7. Magaard, K. and Savin, G., Exceptional Θ-correspondences, Compositio, to appear.Google Scholar
8. Reeder, M., Iwahori spherical discrete series, Annales ENS 27 (1994), 463–491.Google Scholar
9. Savin, G., Dual pair GJ ð PGL2; GJ is the automorphism group of the Jordan algebra J, Invent. Math. 118 (1994), 141–160.Google Scholar
10. Shahidi, F., Langlands’ conjecture on Plancherel measures for p-adic groups. In: Harmonic Analysis on Reductive Groups, Bowdoin College, Birkhauser, 1991.Google Scholar