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Unitary representations of the diffeomorphism group of the p-adic projective line. (English. Russian original) Zbl 0576.22007
Funct. Anal. Appl. 18, 345-346 (1984); translation from Funkts. Anal. Prilozh. 18, No. 4, 92-93 (1984).
The author constructs and studies a series of unitary representations of the group of all local automorphisms of the Bruhat-Tits tree \(J_ p\). Representations of Aut \(J_ p\) were studied by G. I. Ol’shanskij [see Funkts. Anal. Prilozh. 11, No.1, 32-42 (1977; Zbl 0359.22010)].
Reviewer: Yu.Mukhin

MSC:
22A25 Representations of general topological groups and semigroups
05C05 Trees
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[1] G. I. Ol’shanskii, ”Classification of the irreducible representations of the automorphism group of Bruhat?Tits trees,” Funkt. Anal. Prilozhen.,11, No. 1, 32-42 (1977). · Zbl 0359.22010
[2] G. I. Ol’shanskii, ”Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe,” Dokl. Akad. Nauk SSSR,269, No. 1, 33-36 (1983).
[3] Yu. A. Neretin, ”Complementary series of representations of the group of diffeomorphisms of the circle,” Usp. Mat. Nauk,37, No. 2, 213-214 (1982). · Zbl 0533.22013
[4] Yu. A. Neretin, ”Unitary representations with a higher weight of the group of diffeomorphisms of the circle,” Funkts. Anal. Prilozhen.,17, No. 3, 85-86 (1983).
[5] Yu. A. Neretin, ”Boson representation of the diffeomorphism group of the circle,” Dokl. Akad. Nauk SSSR,272, No. 3, 528-531 (1983).
[6] P. Cartier, ”G?ometrie et Analyse sur les arbres,” in: S?minaire Bourbaki, Vol. 1971/1972, 24 ?me Ann?e: Expos?s Nos. 400-417, Lecture Notes in Math.,317, Springer-Verlag, Berlin?New York (1973), pp. 123-140.
[7] Tsuchikawa, ”The Plancherel transform on SL2(k) and its applications to the decomposition of tensor products of irreducible representations,” J. Math. Kyoto Univ.,22, No. 3, 369-433 (1982). · Zbl 0509.22014
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