메뉴 건너뛰기




Volumn 37, Issue 2, 1997, Pages 261-316

Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group or of related permutation groups

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031520421     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250518335     Document Type: Article
Times cited : (8)

References (21)
  • 1
    • 0003273488 scopus 로고
    • Symmetric Hilbert spaces, and related topics
    • Springer-Verlag
    • A. Guichardet, Symmetric Hilbert spaces, and related topics, Lect. Notes in Math., Vol. 261, Springer-Verlag, 1972.
    • (1972) Lect. Notes in Math. , vol.261
    • Guichardet, A.1
  • 3
    • 85033094553 scopus 로고
    • On unitary representations of diffeomorphism groups and those of the infinite symmetric group
    • T. Hirai, On unitary representations of diffeomorphism groups and those of the infinite symmetric group (in Japanese), RIMS Kôkyûroku, Vol. 816, pp. 46-70, 1992.
    • (1992) RIMS Kôkyûroku , vol.816 , pp. 46-70
    • Hirai, T.1
  • 4
    • 0008012385 scopus 로고
    • Irreducible unitary representations of the group of diffeomorphisms of a non-compact manifold
    • T. Hirai, Irreducible unitary representations of the group of diffeomorphisms of a non-compact manifold, J. Math. Kyoto Univ., 33(1993), 827-864.
    • (1993) J. Math. Kyoto Univ. , vol.33 , pp. 827-864
    • Hirai, T.1
  • 5
    • 0038917136 scopus 로고
    • Representations of diffeomorphism groups and the infinite symmetric group
    • Kluwer Academic Publishers
    • T. Hirai, Representations of diffeomorphism groups and the infinite symmetric group, in Noncompact Lie Groups and Some of Their Applications, pp. 225-237, Kluwer Academic Publishers, 1994.
    • (1994) Noncompact Lie Groups and Some of Their Applications , pp. 225-237
    • Hirai, T.1
  • 6
    • 85033088185 scopus 로고    scopus 로고
    • Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group
    • held in Tübingen, Verlag D.+M. Gräbner, Bamberg
    • T. Hirai, Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group, in Transactions of German-Japanese Symposium on 'Infinite-Dimensional Harmonic Analysis' held in Tübingen, pp. 94-112, Verlag D.+M. Gräbner, Bamberg, 1996.
    • (1996) Infinite-Dimensional Harmonic Analysis , pp. 94-112
    • Hirai, T.1
  • 7
    • 0000616816 scopus 로고
    • On equivalence of infinite product measures
    • S. Kakutani, On equivalence of infinite product measures, Ann. Math., 49(1948), 214-224.
    • (1948) Ann. Math. , vol.49 , pp. 214-224
    • Kakutani, S.1
  • 8
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • S. Kerov, G. Ol'shanskiǐ and A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation, C. R. Acad. Sci. Paris, 316(1993), 773-778.
    • (1993) C. R. Acad. Sci. Paris , vol.316 , pp. 773-778
    • Kerov, S.1    Ol'shanskiǐ, G.2    Vershik, A.3
  • 9
    • 0038214555 scopus 로고
    • Unitary representations of the group of diffeomorphisms and of some of its subgroups
    • A. A. Kirillov, Unitary representations of the group of diffeomorphisms and of some of its subgroups, Sci. Math. Sov., 1(1981), 351-372.
    • (1981) Sci. Math. Sov. , vol.1 , pp. 351-372
    • Kirillov, A.A.1
  • 10
    • 84956108415 scopus 로고
    • Holomorphic extensions of representations of the group of diffeomorphisms of the circle
    • Yu. A. Neretin, Holomorphic extensions of representations of the group of diffeomorphisms of the circle, Math. USSR Sbornik, 67(1990), 75-97.
    • (1990) Math. USSR Sbornik , vol.67 , pp. 75-97
    • Neretin, Yu.A.1
  • 11
    • 0038553419 scopus 로고
    • Categories of bistochastic measures, and representations of some infinite-dimensional groups
    • Yu. A. Neretin, Categories of bistochastic measures, and representations of some infinite-dimensional groups, Russian Acad. Sci. Sb. Math., 75(1993), 197-219.
    • (1993) Russian Acad. Sci. Sb. Math. , vol.75 , pp. 197-219
    • Neretin, Yu.A.1
  • 12
    • 0002918036 scopus 로고
    • On infinite direct products
    • J. von Neumann, On infinite direct products, Compositio Math., 6(1938), 1-77.
    • (1938) Compositio Math. , vol.6 , pp. 1-77
    • Von Neumann, J.1
  • 13
    • 0040694811 scopus 로고
    • Certain unitary representations of the infinite symmetric group, I and II
    • N. Obata, Certain unitary representations of the infinite symmetric group, I and II, Nagoya Math. J., 105(1987), 109-119, and 106(1987), 143-162.
    • (1987) Nagoya Math. J. , vol.105 , pp. 109-119
    • Obata, N.1
  • 14
    • 0040694817 scopus 로고
    • N. Obata, Certain unitary representations of the infinite symmetric group, I and II, Nagoya Math. J., 105(1987), 109-119, and 106(1987), 143-162.
    • (1987) Nagoya Math. J. , vol.106 , pp. 143-162
  • 15
    • 0001471212 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. How
    • (Advanced Studies in Comtemporary Mathematics, 7), Gordon and Breach
    • G. I. Ol'shanshiǐ, Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. How, in Representations of Lie groups and related topics. (Advanced Studies in Comtemporary Mathematics, 7), pp. 269-463, Gordon and Breach, 1990.
    • (1990) Representations of Lie Groups and Related Topics , pp. 269-463
    • Ol'shanshiǐ, G.I.1
  • 16
    • 0011022325 scopus 로고
    • Unitary representations of (G, K)-pairs related to the inifinite symmetric group S(∞)
    • G.I. Ol'shanskiǐ, Unitary representations of (G, K)-pairs related to the inifinite symmetric group S(∞), Leningrad Math. J., 1(1990), 983-1014.
    • (1990) Leningrad Math. J. , vol.1 , pp. 983-1014
    • Ol'shanskiǐ, G.I.1
  • 17
    • 0001000050 scopus 로고
    • Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms
    • H. Shimomura, Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms, J. Math. Kyoto Univ., 34(1994), 599-614.
    • (1994) J. Math. Kyoto Univ. , vol.34 , pp. 599-614
    • Shimomura, H.1
  • 18
    • 21344468345 scopus 로고
    • Ergodic decomposition of probability measures on the configuration space
    • H. Shimomura, Ergodic decomposition of probability measures on the configuration space, J. Math. Kyoto Univ., 35(1995), 611-630.
    • (1995) J. Math. Kyoto Univ. , vol.35 , pp. 611-630
    • Shimomura, H.1
  • 19
    • 0002797720 scopus 로고
    • Representations of the group of diffeomorphisms
    • A. M. Vershik, I. M. Gelfand and M. I. Graev, Representations of the group of diffeomorphisms, Usp. Mat. Nauk, 30(1975), 3-50 ( = Russ. Math. Surv., 30(1975), 1-50).
    • (1975) Usp. Mat. Nauk , vol.30 , pp. 3-50
    • Vershik, A.M.1    Gelfand, I.M.2    Graev, M.I.3
  • 20
    • 85033078545 scopus 로고
    • A. M. Vershik, I. M. Gelfand and M. I. Graev, Representations of the group of diffeomorphisms, Usp. Mat. Nauk, 30(1975), 3-50 ( = Russ. Math. Surv., 30(1975), 1-50).
    • (1975) Russ. Math. Surv. , vol.30 , pp. 1-50


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.