Geodesic
On some subspaces in representations of degree two matrix groups with coefficients from a locally compact disconnected field
Sbornik. Mathematics, Tome 17 (1972) no. 3, pp. 357-372 
M. E. Novodvorskii. On some subspaces in representations of degree two matrix groups with coefficients from a locally compact disconnected field. Sbornik. Mathematics, Tome 17 (1972) no. 3, pp. 357-372. http://geodesic.mathdoc.fr/item/SM_1972_17_3_a2/
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     title = {On some subspaces in representations of degree two matrix groups with coefficients from a~locally compact disconnected field},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The commutativity of certain Hecke algebras of subgroups of $\operatorname{PL}(2,F)$ containing the commutator subgroup is established (here $F$ is a discrete normed field with finite field of residues). Application of these results to representations of $p$-adic groups by automorphic forms on the upper complex halfplane allows one to distinguish subrepresentations belonging to the discrete series. Bibliography: 8 titles.

[1] H. Jacquet, R. P. Langlands, “Automorphic forms on $GL(2)$”, Lecture Notes in Math., Springer-Verlag, 1970 | MR | Zbl

[2] J. Dixmier, $C^*$-algebres et leur representations, Paris, 1969 | MR

[3] I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro, Teoriya predstavlenii i avtomorfnye funktsii, Nauka, Moskva, 1966 | MR

[4] R. K. Ganning, “Lektsii o modulyarnykh formakh”, Matematika, 8:6 (1964), 4–68

[5] R. Frike, Die elliptischen Funktionen und ihre Anwendungen, v. II, Leipzig–Berlin, 1922

[6] M. E. Novodvorskii, I. I. Pyatetskii-Shapiro, “Beskonechnomernye abelevy mnogoobraziya i unitarnye predstavleniya grupp”, Matem. sb., 77(119) (1968), 3–20 | MR | Zbl

[7] M. E. Novodvorskii, “O nekotorykh sobstvennykh vektorakh v diskretnykh predstavleniyakh grupp Shevalle”, Matem. sb., 86(128) (1971), 538–551 | MR | Zbl

[8] M. E. Novodvorskii, “O nekotorykh nepodvizhnykh vektorakh v beskonechnomernykh predstavleniyakh grupp Shevalle”, Funkts. analiz, 5:1 (1971), 87–88 | MR | Zbl