메뉴 건너뛰기




Volumn 87, Issue 6, 1997, Pages 3983-4035

Boundary values of holomorphic functions, singular unitary representations of O(p,q), and their limits as q→ ∞

(2)  Neretin, Yu A a   Ol'shanskii, G I a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0012469844     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02355796     Document Type: Article
Times cited : (14)

References (70)
  • 4
    • 0002179766 scopus 로고
    • Quantization in complex symmetric spaces
    • F. A. Berezin, "Quantization in complex symmetric spaces," Izv. Akad. Nauk SSSR, Ser. Mat., 39, No. 2, 1362-1402 (1975).
    • (1975) Izv. Akad. Nauk SSSR, Ser. Mat. , vol.39 , Issue.2 , pp. 1362-1402
    • Berezin, F.A.1
  • 5
    • 0002045160 scopus 로고
    • Representations of SL(2, R) where R is a function ring
    • A. M. Vershik, I. M. Gel'fand, M. I. Graev, "Representations of SL(2, R) where R is a function ring," Usp. Mat. Nauk, 28, No. 5, 83-128 (1973).
    • (1973) Usp. Mat. Nauk , vol.28 , Issue.5 , pp. 83-128
    • Vershik, A.M.1    Gel'fand, I.M.2    Graev, M.I.3
  • 8
    • 53249110754 scopus 로고
    • Linear partial differential equations. Elements of the Classical Theory
    • Yu. V. Egorov and M. A. Shubin, "Linear partial differential equations. Elements of the Classical Theory," Sov. Probl. Mat. Fund. Nap., 30 (1988).
    • (1988) Sov. Probl. Mat. Fund. Nap. , vol.30
    • Egorov Yu., V.1    Shubin, M.A.2
  • 10
    • 53249087374 scopus 로고
    • Exceptional sets in harmonic analysis
    • S. V. Kislyakov, "Exceptional sets in harmonic analysis," Sov. Probl. Mat. Fund. Nap., 42, 199-228 (1988).
    • (1988) Sov. Probl. Mat. Fund. Nap. , vol.42 , pp. 199-228
    • Kislyakov, S.V.1
  • 11
    • 0002418224 scopus 로고
    • Hermitian-positive kernels on homogeneous spaces
    • M. G. Krein, "Hermitian-positive kernels on homogeneous spaces," Ukr. Mat. Zhurn., 1, No. 4, 64-98 (1949).
    • (1949) Ukr. Mat. Zhurn. , vol.1 , Issue.4 , pp. 64-98
    • Krein, M.G.1
  • 12
    • 53249130180 scopus 로고
    • Restriction of the complementary series representation to the pseudoorthogonal group of a lower dimension
    • B. F. Molchanov, "Restriction of the complementary series representation to the pseudoorthogonal group of a lower dimension," Dokl. Akad. Nauk SSSR, 237, No. 4 (1977).
    • (1977) Dokl. Akad. Nauk SSSR , vol.237 , Issue.4
    • Molchanov, B.F.1
  • 13
    • 0010863146 scopus 로고
    • Plancherel formula for hyperboloid
    • V. F. Molchanov, "Plancherel formula for hyperboloid," Tr. Mat. Inst. Steklov, 147, 65-85 (1980).
    • (1980) Tr. Mat. Inst. Steklov , vol.147 , pp. 65-85
    • Molchanov, V.F.1
  • 14
    • 0002027921 scopus 로고
    • Harmonic analysis on homogeneous spaces
    • V. F. Molchanov, "Harmonic analysis on homogeneous spaces," Sov. Probl. Mat. Fund. Nap., 59, 5-144 (1990).
    • (1990) Sov. Probl. Mat. Fund. Nap. , vol.59 , pp. 5-144
    • Molchanov, V.F.1
  • 15
    • 33846868528 scopus 로고
    • Decomposition of the tensor product of irreducible representations of the proper Lorentz group into irreducible components III
    • M. A. Naimark, "Decomposition of the tensor product of irreducible representations of the proper Lorentz group into irreducible components III," Tr. Mosk. Mat. Obshch., 10, 181-216 (1961).
    • (1961) Tr. Mosk. Mat. Obshch. , vol.10 , pp. 181-216
    • Naimark, M.A.1
  • 16
    • 0009177323 scopus 로고
    • On discrete occurences of the complement series representations in a tensor product of unitary representations
    • Yu. A. Neretin, "On discrete occurences of the complement series representations in a tensor product of unitary representations," Funk. Anal. Pril., 20, No. 1, 79-80 (1986).
    • (1986) Funk. Anal. Pril. , vol.20 , Issue.1 , pp. 79-80
    • Neretin Yu., A.1
  • 17
    • 0347904077 scopus 로고
    • Representations of the Virasoro algebra and of affine algebras
    • Yu. A. Neretin, "Representations of the Virasoro algebra and of affine algebras," Sov. Probl. Mat. Fund. Nap., 22, 163-224 (1988).
    • (1988) Sov. Probl. Mat. Fund. Nap. , vol.22 , pp. 163-224
    • Neretin Yu., A.1
  • 18
    • 0010804532 scopus 로고
    • On a semigroup of operators in the boson Fock space
    • Yu. A. Neretin, "On a semigroup of operators in the boson Fock space," Funkt. Anal. Pril., 24, No. 2, 63-73 (1990).
    • (1990) Funkt. Anal. Pril. , vol.24 , Issue.2 , pp. 63-73
    • Neretin Yu., A.1
  • 19
    • 34250284168 scopus 로고
    • 0(p, ∞), Sp (p, ∞) in the corresponding motion groups
    • 0(p, ∞), Sp (p, ∞) in the corresponding motion groups," Funkt. Anal. Pril., 12, No. 3, 32-44 (1978).
    • (1978) Funkt. Anal. Pril. , vol.12 , Issue.3 , pp. 32-44
    • Ol'shanskii, G.I.1
  • 20
    • 22544484034 scopus 로고
    • Description of the highest weight unitary representations for groups U(p, q)∼
    • G. I. Ol'shanskii, "Description of the highest weight unitary representations for groups U(p, q)∼," Funkt. Anal. Pril., 14, No. 3, 32-44 (1980).
    • (1980) Funkt. Anal. Pril. , vol.14 , Issue.3 , pp. 32-44
    • Ol'shanskii, G.I.1
  • 21
    • 0442304991 scopus 로고
    • Infinite-dimensional classical groups of finite R-rank: A description of representations and asymptotic theory
    • G. I. Ol'shanskii, "Infinite-dimensional classical groups of finite R-rank: a description of representations and asymptotic theory," Funkt. Anal. Pril., 18, No. 1, 28-42 (1984).
    • (1984) Funkt. Anal. Pril. , vol.18 , Issue.1 , pp. 28-42
    • Ol'shanskii, G.I.1
  • 22
    • 0008827076 scopus 로고
    • Irreducible unitary represrntations of the groups U(p, q) which admit the pass to the limit as q → ∞
    • G. I. Ol'shanskii, "Irreducible unitary represrntations of the groups U(p, q) which admit the pass to the limit as q → ∞," Zap. Nauchn. Semin. LOMI, 172, 114-120 (1989).
    • (1989) Zap. Nauchn. Semin. LOMI , vol.172 , pp. 114-120
    • Ol'shanskii, G.I.1
  • 25
    • 0003449868 scopus 로고
    • Springer-Verlag, Berlin
    • N, Springer-Verlag, Berlin (1980).
    • (1980) N
    • Rudin, W.1
  • 30
    • 0040324064 scopus 로고
    • Discrete spectrum of reductive dual pair (O(p, q), Sp(2m))
    • J. D. Adams, "Discrete spectrum of reductive dual pair (O(p, q), Sp(2m))," Inv. Math., 74, 449-475 (1983).
    • (1983) Inv. Math. , vol.74 , pp. 449-475
    • Adams, J.D.1
  • 32
    • 0001235633 scopus 로고
    • Irreducible unitary representations of Lorentz group
    • V. Bargmann, "Irreducible unitary representations of Lorentz group," Ann. Math., 48, 568-640 (1947).
    • (1947) Ann. Math. , vol.48 , pp. 568-640
    • Bargmann, V.1
  • 33
  • 34
    • 52449141029 scopus 로고
    • Sur les domaines bornés homogènes de l'espace de n variables complexes
    • E. Cartan, "Sur les domaines bornés homogènes de l'espace de n variables complexes," Abhandl. Mat. Semin Univ. Hamburg, 116-162 (1936).
    • (1936) Abhandl. Mat. Semin Univ. Hamburg , pp. 116-162
    • Cartan, E.1
  • 36
    • 0000698473 scopus 로고
    • Discrete series for semisimple symmetric spaces
    • M. Flensted-Jensen, "Discrete series for semisimple symmetric spaces," Ann. Math., 111, 253-311 (1980).
    • (1980) Ann. Math. , vol.111 , pp. 253-311
    • Flensted-Jensen, M.1
  • 37
    • 0000738071 scopus 로고
    • Representations of semisimple Lie groups IV
    • Harish-Chandra, "Representations of semisimple Lie groups IV," Am. J. Math., 743-777 (1955).
    • (1955) Am. J. Math. , pp. 743-777
    • Harish-Chandra1
  • 38
    • 0001273096 scopus 로고
    • On some results of Strichartz and of Rallis and Schiffmann
    • R. Howe, "On some results of Strichartz and of Rallis and Schiffmann," J. Funct. Anal., 32, 297-303 (1979).
    • (1979) J. Funct. Anal. , vol.32 , pp. 297-303
    • Howe, R.1
  • 39
    • 0001833206 scopus 로고
    • On the Segal-Shale-Weil representation and the harmonic polynomials
    • M. Kashiwara and M. Vergne, "On the Segal-Shale-Weil representation and the harmonic polynomials," Inv. Math., 44, 1-47 (1978).
    • (1978) Inv. Math. , vol.44 , pp. 1-47
    • Kashiwara, M.1    Vergne, M.2
  • 41
    • 0041802960 scopus 로고
    • Singular unitary representations and discrete series for indefinite Stiefel manifolds U(p, q; double-struck F sign )/U(p - M, q; double-struck F sign)
    • T. Kobayashi, "Singular unitary representations and discrete series for indefinite Stiefel manifolds U(p, q; double-struck F sign)/U(p - m, q; double-struck F sign)," Mem. AMS, 95 (1992).
    • (1992) Mem. AMS , vol.95
    • Kobayashi, T.1
  • 42
    • 53249083465 scopus 로고
    • Mantles, trains and representations of infinite dimensional groups
    • Birkhauser, Boston
    • Yu. A. Neretin, "Mantles, trains and representations of infinite dimensional groups," First European Congress of Mathematics, Vol. 2, Birkhauser, Boston (1994), pp. 293-310.
    • (1994) First European Congress of Mathematics , vol.2 , pp. 293-310
    • Neretin Yu., A.1
  • 44
    • 0001471212 scopus 로고
    • Unitary representation of infinite dimensional pairs (G, K) and the formalism of R. Howe
    • Gordon and Breach
    • G. I. Ol'shanskii, "Unitary representation of infinite dimensional pairs (G, K) and the formalism of R. Howe," in: Representations of Lie Groups and Related Topics, Gordon and Breach, (1990), pp. 269-464.
    • (1990) Representations of Lie Groups and Related Topics , pp. 269-464
    • Ol'shanskii, G.I.1
  • 45
    • 84951211512 scopus 로고
    • On the Kronecker products of irreducible representations of 2 × 2 real unimodular group I
    • L. Pukanszky, "On the Kronecker products of irreducible representations of 2 × 2 real unimodular group I," Trans. Am. Math. Soc., 100, No. 1, 116-152 (1961).
    • (1961) Trans. Am. Math. Soc. , vol.100 , Issue.1 , pp. 116-152
    • Pukanszky, L.1
  • 46
    • 0002756688 scopus 로고
    • Singular unitary representations and indefinite harmonic theory
    • J. Rawnsley, W. Schmid, and J. A. Wolf, "Singular unitary representations and indefinite harmonic theory," J. Funct. Anal., 51, 1-114 (1983).
    • (1983) J. Funct. Anal. , vol.51 , pp. 1-114
    • Rawnsley, J.1    Schmid, W.2    Wolf, J.A.3
  • 47
    • 34250389976 scopus 로고
    • Analytic continuation of the holomorphic discrete series of a semisimple Lie group
    • H. Rossi and M. Vergne, "Analytic continuation of the holomorphic discrete series of a semisimple Lie group," Acta Math., 136, No. 1-2, 1-59 (1976).
    • (1976) Acta Math. , vol.136 , Issue.1-2 , pp. 1-59
    • Rossi, H.1    Vergne, M.2
  • 48
    • 0000602260 scopus 로고
    • A series of unitary irreducible representations induced from symmetric subgroup of a semisimple Lie group
    • H. Schlichtkrull, "A series of unitary irreducible representations induced from symmetric subgroup of a semisimple Lie group," Inv. Math., 68, 497-516 (1982).
    • (1982) Inv. Math. , vol.68 , pp. 497-516
    • Schlichtkrull, H.1
  • 49
    • 0001751659 scopus 로고
    • Harmonic analysis on hyperboloids
    • S. Strichartz, "Harmonic analysis on hyperboloids," J. Funct. Anal., 12, 341-383 (1973).
    • (1973) J. Funct. Anal. , vol.12 , pp. 341-383
    • Strichartz, S.1
  • 50
    • 53249145271 scopus 로고
    • 2(k) and its application to tensor products of irreducible representations
    • 2(k) and its application to tensor products of irreducible representations," J. Math. Kyoto Univ., 22, No. 3, 369-437 (1982).
    • (1982) J. Math. Kyoto Univ. , vol.22 , Issue.3 , pp. 369-437
    • Tsuchikawa1
  • 51
    • 84968467363 scopus 로고
    • Analytic continuation of discrete series
    • N. R. Wallach, "Analytic continuation of discrete series," Trans. Am. Math. Soc., 251, 19-37 (1979).
    • (1979) Trans. Am. Math. Soc. , vol.251 , pp. 19-37
    • Wallach, N.R.1
  • 52
    • 0000142609 scopus 로고
    • Inequalities between two kinds of eigenvalues of linear transformation
    • H. Weyl, "Inequalities between two kinds of eigenvalues of linear transformation," Proc. Nat. Acad. Sci., 35, 408-411 (1949).
    • (1949) Proc. Nat. Acad. Sci. , vol.35 , pp. 408-411
    • Weyl, H.1
  • 53
    • 0000993306 scopus 로고
    • Tensor products of infinite dimensional and finite dimensional representations of semisimple Lie group
    • G. Zuckerman, "Tensor products of infinite dimensional and finite dimensional representations of semisimple Lie group," Ann. Math., 106, 295-308 (1977).
    • (1977) Ann. Math. , vol.106 , pp. 295-308
    • Zuckerman, G.1
  • 56
    • 0008829447 scopus 로고
    • Invariant distributions in homogeneous domains
    • S. G. Gindikin, "Invariant distributions in homogeneous domains," Funkt. Anal. Pril., 9, No. 1, 56-58 (1975).
    • (1975) Funkt. Anal. Pril. , vol.9 , Issue.1 , pp. 56-58
    • Gindikin, S.G.1
  • 57
    • 0039881230 scopus 로고
    • The last possible place of unitarity for certain highest weight modules
    • H. P. Jakobsen, "The last possible place of unitarity for certain highest weight modules," Math. Ann., 256, 439-447 (1981).
    • (1981) Math. Ann. , vol.256 , pp. 439-447
    • Jakobsen, H.P.1
  • 59
    • 0037539090 scopus 로고
    • Principal representations of the group U(∞)
    • A. M. Vershik and D. P. Zhelobenko (eds.), Gordon and Breach
    • I. M. Gelfand and M. I. Graev, "Principal representations of the group U(∞)," in: Representations of Lie Groups and Related Topics, A. M. Vershik and D. P. Zhelobenko (eds.), Gordon and Breach (1993), pp. 119-154.
    • (1993) Representations of Lie Groups and Related Topics , pp. 119-154
    • Gelfand, I.M.1    Graev, M.I.2
  • 60
    • 0009325654 scopus 로고
    • Restrictions and expansions of holomorphic representations
    • H. P. Jakobsen and M. Vergne, "Restrictions and expansions of holomorphic representations," J. Funct. Anal., 34, 29-53 (1979).
    • (1979) J. Funct. Anal. , vol.34 , pp. 29-53
    • Jakobsen, H.P.1    Vergne, M.2
  • 61
    • 0001498468 scopus 로고
    • Distributions spheriques sur les espaces hyperboliques
    • J. Faraut, "Distributions spheriques sur les espaces hyperboliques," J. Math. Pures Appl., 58, 369-444 (1979).
    • (1979) J. Math. Pures Appl. , vol.58 , pp. 369-444
    • Faraut, J.1
  • 62
    • 0000607396 scopus 로고
    • Representations of the pseudoorthogonal group related to a cone
    • V. F. Molchanov, "Representations of the pseudoorthogonal group related to a cone," Mat. Sb., 81, 358-375 (1970).
    • (1970) Mat. Sb. , vol.81 , pp. 358-375
    • Molchanov, V.F.1
  • 63
    • 0000993962 scopus 로고
    • q(λ) with respect to reductive subgroups and its applications
    • q(λ) with respect to reductive subgroups and its applications," Inv. Math., 117, 181-205 (1994).
    • (1994) Inv. Math. , vol.117 , pp. 181-205
    • Kobayashi, T.1
  • 64
    • 53249132139 scopus 로고
    • On representations of the Lorentz group which are unitary in an indefinite metric
    • R. S. Ismagilov, "On representations of the Lorentz group which are unitary in an indefinite metric," Tr. MIEM, 2, 492-504 (1966).
    • (1966) Tr. MIEM , vol.2 , pp. 492-504
    • Ismagilov, R.S.1
  • 67
    • 0000936358 scopus 로고
    • An intrinsic analysis of unititarizable nighest weight modules
    • T. J. Enright and A. Joseph, "An intrinsic analysis of unititarizable nighest weight modules," Math. Ann., 288, 571-594 (1990).
    • (1990) Math. Ann. , vol.288 , pp. 571-594
    • Enright, T.J.1    Joseph, A.2
  • 68
    • 0010178849 scopus 로고
    • Annihilators and associated weight modules
    • A. Joseph, "Annihilators and associated weight modules," Ann. Sci. Ecole Norm. Sup., 25, 1-45 (1992).
    • (1992) Ann. Sci. Ecole Norm. Sup. , vol.25 , pp. 1-45
    • Joseph, A.1
  • 69
    • 0000745277 scopus 로고
    • On tensor product of finite and infinite dimensional representations
    • B. Kostant, "On tensor product of finite and infinite dimensional representations," J. Funct. Anal., 20, 257-285 (1975).
    • (1975) J. Funct. Anal. , vol.20 , pp. 257-285
    • Kostant, B.1
  • 70
    • 0010954950 scopus 로고
    • Inequalities for Strongly Singular convolution operators
    • C. Fefferman, "Inequalities for Strongly Singular convolution operators," Acta Math., 124, 9-36 (1970).
    • (1970) Acta Math. , vol.124 , pp. 9-36
    • Fefferman, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.