A note on the local theta correspondence for unitary similitude dual pairs. (English) Zbl 1295.22026
Summary: Following B. Roberts’ work [Isr. J. Math. 94, 285–317 (1996; Zbl 0870.22011)] in the case of orthogonal-symplectic similitude dual pairs, we study the local theta correspondence for unitary similitude dual pairs over a \(p\)-adic field.
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
Citations:
Zbl 0870.22011References:
| [1] | Barthel, L., Local Howe correspondence for groups of similitudes, J. Reine Angew. Math., 414, 207-220 (1991) · Zbl 0708.22006 |
| [2] | W.T. Gan, W. Tantono, The local Langlands conjecture for \(\operatorname{GSp}(4)\); W.T. Gan, W. Tantono, The local Langlands conjecture for \(\operatorname{GSp}(4)\) · Zbl 1298.11043 |
| [3] | Harris, M., L-functions of \(2 \times 2\) unitary groups and factorization of periods of Hilbert modular forms, J. Amer. Math. Soc., 6, 637-719 (1993) · Zbl 0779.11023 |
| [4] | Harris, M., Cohomological automorphic forms on unitary groups, II: Period relations and values of L-functions, (Harmonic analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honor of Roger E. Howe. Harmonic analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honor of Roger E. Howe, Lect. Notes Ser. Inst. Math. Sci., vol. 12 (2007), National University of Singapore, World Scientific Publishing), 89-149 · Zbl 1390.11088 |
| [5] | Harris, M.; Kudla, S.; Sweet, S., Theta dichotomy for unitary groups, J. Amer. Math. Soc., 9, 941-1004 (1996) · Zbl 0870.11026 |
| [6] | Kudla, S., Splitting metaplectic covers of dual reductive pairs, Israel J. Math., 87, 361-401 (1994) · Zbl 0840.22029 |
| [7] | Moeglin, C.; Vigénras, M.-F.; Waldspurger, J.-L., Correspondances de Howe sur un corps \(p\)-adique, Lecture Notes in Math., vol. 1291 (1987), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York · Zbl 0642.22002 |
| [8] | Rao, R. R., On some explicit formulas in the theory of Weil representation, Pacific J. Math., 157, 335-371 (1993) · Zbl 0794.58017 |
| [9] | Roberts, B., The theta correspondence for similitudes, Israel J. Math., 94, 285-317 (1996) · Zbl 0870.22011 |
| [10] | Sun, B.; Zhu, C.-B., Conservation relations for local theta correspondence · Zbl 1321.22017 |
| [11] | Waldspurger, J.-L., Démonstration dʼune conjecture de dualité de Howe dans le cas \(p\)-adique, \(p \neq 2\), (Festschrift in honor of Piatetski-Shapiro. Festschrift in honor of Piatetski-Shapiro, Israel Math. Conf. Proc., vol. 2 (1990)), 267-324 · Zbl 0722.22009 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
