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Volumn 236, Issue 2, 2006, Pages 634-681

Quasiregular representations of the infinite-dimensional nilpotent group

Author keywords

Gaussian measures; Infinite tensor products; Infinite dimensional groups; Irreducibility; Ismagilov conjecture; Nilpotent groups; Quasiregular representations

Indexed keywords


EID: 33646355676     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.03.013     Document Type: Article
Times cited : (5)

References (40)
  • 1
    • 0002171899 scopus 로고
    • The energy representation of Sobolev-Lie group
    • Albeverio S., and Höegh-Krohn R. The energy representation of Sobolev-Lie group. Compos. Math. 36 (1978) 37-52
    • (1978) Compos. Math. , vol.36 , pp. 37-52
    • Albeverio, S.1    Höegh-Krohn, R.2
  • 2
    • 11044224587 scopus 로고    scopus 로고
    • Quasiregular representations of the infinite-dimensional Borel group
    • Albeverio S., and Kosyak A. Quasiregular representations of the infinite-dimensional Borel group. J. Funct. Anal. 218 2 (2005) 445-474
    • (2005) J. Funct. Anal. , vol.218 , Issue.2 , pp. 445-474
    • Albeverio, S.1    Kosyak, A.2
  • 3
    • 33646381416 scopus 로고    scopus 로고
    • Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group
    • Albeverio S., and Kosyak A. Group action, quasi-invariant measures and quasiregular representations of the infinite-dimensional nilpotent group. Contemp. Math. 385 (2005) 259-280
    • (2005) Contemp. Math. , vol.385 , pp. 259-280
    • Albeverio, S.1    Kosyak, A.2
  • 4
    • 0001036206 scopus 로고
    • Irreducibility and reducibility for the energy representation of a group of mapping of a Riemannian manifold into a compact Lie group
    • Albeverio S., Höegh-Krohn R., and Testard D. Irreducibility and reducibility for the energy representation of a group of mapping of a Riemannian manifold into a compact Lie group. J. Funct. Anal. 41 (1981) 378-396
    • (1981) J. Funct. Anal. , vol.41 , pp. 378-396
    • Albeverio, S.1    Höegh-Krohn, R.2    Testard, D.3
  • 14
    • 0011044966 scopus 로고
    • Representations of the group of smooth mappings in a compact Lie group
    • (in Russian)
    • Ismagilov R.S. Representations of the group of smooth mappings in a compact Lie group. Funkts. Anal. i Priložhen. 15 2 (1981) 73-74 (in Russian)
    • (1981) Funkts. Anal. i Priložhen. , vol.15 , Issue.2 , pp. 73-74
    • Ismagilov, R.S.1
  • 15
    • 0000616816 scopus 로고
    • On equivalence of infinite product measures
    • Kakutani S. On equivalence of infinite product measures. Ann. of Math. 4 (1948) 214-224
    • (1948) Ann. of Math. , vol.4 , pp. 214-224
    • Kakutani, S.1
  • 16
    • 0003219350 scopus 로고
    • Elements of the Theory of Representations
    • Springer, Berlin (translated from the Russian)
    • Kirillov A.A. Elements of the Theory of Representations. Grundlehren Math. Wiss. vol. 220 (1976), Springer, Berlin (translated from the Russian)
    • (1976) Grundlehren Math. Wiss. , vol.220
    • Kirillov, A.A.1
  • 17
    • 11044225306 scopus 로고
    • Introduction to the theory of representations and noncommutative harmonic analysis
    • Representation Theory and Noncommutative Harmonic Analysis, I, Springer, Berlin
    • Kirillov A.A. Introduction to the theory of representations and noncommutative harmonic analysis. Representation Theory and Noncommutative Harmonic Analysis, I. Encyclopaedia Math. Sci. vol. 22 (1994), Springer, Berlin 1-156
    • (1994) Encyclopaedia Math. Sci. , vol.22 , pp. 1-156
    • Kirillov, A.A.1
  • 18
    • 33646358539 scopus 로고
    • Irreducibility criterion for regular Gaussian representations of group of finite upper triangular matrices
    • (in Russian); transl. in:
    • Kosyak A.V. Irreducibility criterion for regular Gaussian representations of group of finite upper triangular matrices. Funkts. Anal. i Priložhen. 24 3 (1990) 82-83 (in Russian); transl. in:
    • (1990) Funkts. Anal. i Priložhen. , vol.24 , Issue.3 , pp. 82-83
    • Kosyak, A.V.1
  • 19
    • 33646358539 scopus 로고
    • Irreducibility criterion for regular Gaussian representations of group of finite upper triangular matrices
    • Kosyak A.V. Irreducibility criterion for regular Gaussian representations of group of finite upper triangular matrices. Funct. Anal. Appl. 24 3 (1990) 243-245
    • (1990) Funct. Anal. Appl. , vol.24 , Issue.3 , pp. 243-245
    • Kosyak, A.V.1
  • 20
    • 0011029615 scopus 로고
    • Criteria for irreducibility and equivalence of regular Gaussian representations of group of finite upper triangular matrices of infinite order
    • Kosyak A.V. Criteria for irreducibility and equivalence of regular Gaussian representations of group of finite upper triangular matrices of infinite order. Selecta Math. Soviet. 11 (1992) 241-291
    • (1992) Selecta Math. Soviet. , vol.11 , pp. 241-291
    • Kosyak, A.V.1
  • 21
    • 0000221024 scopus 로고
    • Irreducible regular Gaussian representations of the group of the interval and the circle diffeomorphisms
    • Kosyak A.V. Irreducible regular Gaussian representations of the group of the interval and the circle diffeomorphisms. J. Funct. Anal. 125 (1994) 493-547
    • (1994) J. Funct. Anal. , vol.125 , pp. 493-547
    • Kosyak, A.V.1
  • 22
    • 0347551001 scopus 로고    scopus 로고
    • Regular representations of the group of finite upper-triangular matrices, corresponding to product measures, and criteria for their irreducibility
    • Kosyak A.V. Regular representations of the group of finite upper-triangular matrices, corresponding to product measures, and criteria for their irreducibility. Methods Funct. Anal. Topology 6 (2000) 43-65
    • (2000) Methods Funct. Anal. Topology , vol.6 , pp. 43-65
    • Kosyak, A.V.1
  • 25
    • 33646359014 scopus 로고    scopus 로고
    • A criterion for irreducibility of quasiregular representations of the group of finite upper-triangular matrices
    • (in Russian); transl. in:
    • Kosyak A.V. A criterion for irreducibility of quasiregular representations of the group of finite upper-triangular matrices. Funkts. Anal. i Priložhen. 37 1 (2003) 78-81 (in Russian); transl. in:
    • (2003) Funkts. Anal. i Priložhen. , vol.37 , Issue.1 , pp. 78-81
    • Kosyak, A.V.1
  • 26
    • 0037249308 scopus 로고    scopus 로고
    • A criterion for irreducibility of quasiregular representations of the group of finite upper-triangular matrices
    • Kosyak A.V. A criterion for irreducibility of quasiregular representations of the group of finite upper-triangular matrices. Funct. Anal. Appl. 37 1 (2003) 65-68
    • (2003) Funct. Anal. Appl. , vol.37 , Issue.1 , pp. 65-68
    • Kosyak, A.V.1
  • 27
    • 3543062302 scopus 로고    scopus 로고
    • Quasi-invariant measures and irreducible representations of the inductive limit of the special linear groups
    • (in Russian); transl. in:
    • Kosyak A.V. Quasi-invariant measures and irreducible representations of the inductive limit of the special linear groups. Funkts. Anal. i Priložhen. 38 1 (2004) 82-84 (in Russian); transl. in:
    • (2004) Funkts. Anal. i Priložhen. , vol.38 , Issue.1 , pp. 82-84
    • Kosyak, A.V.1
  • 28
    • 3543062302 scopus 로고    scopus 로고
    • Quasi-invariant measures and irreducible representations of the inductive limit of the special linear groups
    • Kosyak A.V. Quasi-invariant measures and irreducible representations of the inductive limit of the special linear groups. Funct. Anal. Appl. 38 1 (2004) 67-68
    • (2004) Funct. Anal. Appl. , vol.38 , Issue.1 , pp. 67-68
    • Kosyak, A.V.1
  • 29
    • 0003225839 scopus 로고
    • Gaussian Measures in Banach Spaces
    • Springer, Berlin
    • Kuo H.H. Gaussian Measures in Banach Spaces. Lecture Notes in Math. vol. 463 (1975), Springer, Berlin
    • (1975) Lecture Notes in Math. , vol.463
    • Kuo, H.H.1
  • 30
    • 0035586151 scopus 로고    scopus 로고
    • A converse to the Jensen inequality, its matrix extensions and inequalities for minors and eigenvalues
    • Malamud S.M. A converse to the Jensen inequality, its matrix extensions and inequalities for minors and eigenvalues. Linear Algebra Appl. 322 1-3 (2001) 19-41
    • (2001) Linear Algebra Appl. , vol.322 , Issue.1-3 , pp. 19-41
    • Malamud, S.M.1
  • 31
    • 0010872067 scopus 로고
    • Naturality of quasi-invariance of some measures
    • Stochastic Analysis and Applications. Cruzeiro A.B., and Zambrini J.-C. (Eds). Lisbon, 1989, Birkhäuser Boston, Boston, MA
    • Malliavin M.P. Naturality of quasi-invariance of some measures. In: Cruzeiro A.B., and Zambrini J.-C. (Eds). Stochastic Analysis and Applications. Lisbon, 1989. Progress in Probability vol. 26 (1991), Birkhäuser Boston, Boston, MA 144-154
    • (1991) Progress in Probability , vol.26 , pp. 144-154
    • Malliavin, M.P.1
  • 32
    • 25444446587 scopus 로고    scopus 로고
    • Probability and geometry
    • Taniguchi Conference on Mathematics, Nara'98, Math. Soc. Japan, Tokyo
    • Malliavin M.P. Probability and geometry. Taniguchi Conference on Mathematics, Nara'98. Adv. Stud. Pure Math. vol. 31 (2001), Math. Soc. Japan, Tokyo 179-209
    • (2001) Adv. Stud. Pure Math. , vol.31 , pp. 179-209
    • Malliavin, M.P.1
  • 33
    • 0010968183 scopus 로고
    • Measures quasi invariantes sur certain groupes de dimension infinie
    • Malliavin M.P., and Malliavin P. Measures quasi invariantes sur certain groupes de dimension infinie. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 765-768
    • (1990) C. R. Acad. Sci. Paris Sér. I Math. , vol.311 , pp. 765-768
    • Malliavin, M.P.1    Malliavin, P.2
  • 35
    • 0001918078 scopus 로고
    • Integration on loop groups, III: Asymptotic Peter-Weyl orthogonality
    • Malliavin M.P., and Malliavin P. Integration on loop groups, III: Asymptotic Peter-Weyl orthogonality. J. Funct. Anal. 108 (1992) 13-46
    • (1992) J. Funct. Anal. , vol.108 , pp. 13-46
    • Malliavin, M.P.1    Malliavin, P.2
  • 36
    • 33646382896 scopus 로고
    • Examples of factor-representations of the group GL ( ∞ )
    • Naukova Dumka, Kiev (in Russian)
    • Nessonov N.I. Examples of factor-representations of the group GL ( ∞ ). Mathematical Physics, Functional Analysis (1986), Naukova Dumka, Kiev 48-52 (in Russian)
    • (1986) Mathematical Physics, Functional Analysis , pp. 48-52
    • Nessonov, N.I.1


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