×

Residual automorphic representations of \(Sp_ 4\). (English) Zbl 0788.11019

The author studies the decomposition of \(L^ 2(G(F)\setminus G(\mathbb{A}_ F))\), where \(G=Sp_ 4\) is the symplectic group of degree 2 defined over an algebraic number field \(F\). By the general theory of Eisenstein series (as developed by Langlands), this decomposition has components associated with certain parabolic subgroups of \(G\). The author considers the residual (i.e. discrete) part of that component associated to the Borel subgroup of \(G\). He conjectures that by taking resdues of Eisenstein series based on representations induced off of nontrivial quadratic characters on the Borel subgroup, one produces nontrivial intertwining operators whose images are irreducible and multiplicity free within this component. Part of the conjecture is examined in the case where the character has square free conductor.

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Compositio Math 58 pp 233– (1986)
[2] Trans. Amer. Math. Soc 131 pp 488– (1968)
[3] (1981)
[4] Proc. Sympo. Pure Math. Amer. Math. Soc 33 pp 203– (1979)
[5] Contemporary Math. 53. Amer. Math. Soc pp 253– (1986)
[6] Lecture Notes in Math. 544 (1976)
[7] Lecture Notes in Math., 62 (1968)
[8] DOI: 10.3792/pjaa.63.114 · Zbl 0623.10017 · doi:10.3792/pjaa.63.114
[9] Osaka J. Math 9 pp 75– (1972)
[10] DOI: 10.1080/00927878008822475 · Zbl 0438.20029 · doi:10.1080/00927878008822475
[11] Bull. Soc. Math. France 107 pp 55– (1979)
[12] DOI: 10.1016/0021-8693(76)90054-5 · Zbl 0328.20037 · doi:10.1016/0021-8693(76)90054-5
[13] DOI: 10.1007/BF01110070 · Zbl 0185.06801 · doi:10.1007/BF01110070
[14] (1984)
[15] I.H.E.S. Publ. Math 40 pp 81– (1972)
[16] DOI: 10.1007/BF01390139 · Zbl 0334.22012 · doi:10.1007/BF01390139
[17] Proc. Symp. Pure Math. Amer. Math. Soc 33 pp 253– (1979)
[18] J. Math. Kyoto Univ 28 pp 343– (1988) · Zbl 0692.10025 · doi:10.1215/kjm/1250520487
[19] J. reine angew. Math 343 pp 184– (1983)
[20] Bull. Soc. Math. France 116 pp 15– (1988) · Zbl 0662.22011 · doi:10.24033/bsmf.2088
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.