메뉴 건너뛰기




Volumn 174, Issue 2, 1996, Pages 497-542

Coherent states, holomorphic extensions, and highest weight representations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001445180     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1996.174.497     Document Type: Article
Times cited : (27)

References (42)
  • 2
  • 3
    • 0039433260 scopus 로고
    • Complex extensions of the representation of the symplectic group associated with the canonical commutation relations
    • M. Brunet and P. Kramer, Complex extensions of the representation of the symplectic group associated with the canonical commutation relations, Reports on Math. Physics, 17 (1980), 205-215.
    • (1980) Reports on Math. Physics , vol.17 , pp. 205-215
    • Brunet, M.1    Kramer, P.2
  • 4
    • 0038840564 scopus 로고
    • The metaplectic semigroup and related topics
    • M. Brunet, The metaplectic semigroup and related topics, Reports on Math. Physics, 22 (1985), 149-170.
    • (1985) Reports on Math. Physics , vol.22 , pp. 149-170
    • Brunet, M.1
  • 6
    • 0002900117 scopus 로고
    • The fundamental conjecture for homogeneous Kähler manifolds
    • J. Dorfmeister and K. Nakajima, The fundamental conjecture for homogeneous Kähler manifolds, Acta. Math., 161 (1988), 23-70.
    • (1988) Acta Math. , vol.161 , pp. 23-70
    • Dorfmeister, J.1    Nakajima, K.2
  • 8
    • 0003185113 scopus 로고
    • T.J. Enright, R. Howe and N. Wallach, A classification of unitary highest weight modules, Proc. Representation theory of reductive groups (Park City, UT, 1982), pp. 97-149; Progr. Math., 40 (1983), 97-143.
    • (1983) Progr. Math. , vol.40 , pp. 97-143
  • 11
    • 0000738071 scopus 로고
    • Representations of semi-simple Lie groups, IV
    • Harish-Chandra, Representations of semi-simple Lie groups, IV, Amer. J. Math., 77 (1955), 743-777.
    • (1955) Amer. J. Math. , vol.77 , pp. 743-777
    • Harish-Chandra1
  • 12
    • 0000964209 scopus 로고
    • Representations of semi-simple Lie groups, VI
    • _, Representations of semi-simple Lie groups, VI, Amer. J. Math., 78 (1956), 564-628.
    • (1956) Amer. J. Math. , vol.78 , pp. 564-628
  • 13
    • 0013200611 scopus 로고
    • A note on Howe's oscillator semigroup
    • J. Hilgert, A note on Howe's oscillator semigroup, Annales de l'institut Fourier, 39 (1989), 663-688.
    • (1989) Annales de L'Institut Fourier , vol.39 , pp. 663-688
    • Hilgert, J.1
  • 16
    • 0003284771 scopus 로고
    • Lie semigroups and their applications
    • Springer
    • _, Lie semigroups and their applications, Lecture Notes in Math., 1552, Springer, 1993.
    • (1993) Lecture Notes in Math. , vol.1552
  • 17
    • 0002347671 scopus 로고
    • Symplectic convexity theorems and coadjoint orbits
    • J. Hilgert, K.-H. Neeb and W. Plank, Symplectic convexity theorems and coadjoint orbits, Comp. Math., 94 (1994), 129-180.
    • (1994) Comp. Math. , vol.94 , pp. 129-180
    • Hilgert, J.1    Neeb, K.-H.2    Plank, W.3
  • 18
    • 0011616669 scopus 로고
    • Analytic continuations of representations, the solvable case
    • J. Hilgert and G. Olafsson, Analytic continuations of representations, the solvable case, Jap. Journal of Math., 18 (1992), 213-290.
    • (1992) Jap. Journal of Math. , vol.18 , pp. 213-290
    • Hilgert, J.1    Olafsson, G.2
  • 19
    • 0002617763 scopus 로고
    • The Oscillator semigroup
    • The Mathematical Heritage of Hermann Weyl, R. O. Wells ed., AMS Providence
    • R. Howe, The Oscillator semigroup, in "The Mathematical Heritage of Hermann Weyl", Proc. Symp. Pure Math., 48, R. O. Wells ed., AMS Providence, 1988.
    • (1988) Proc. Symp. Pure Math. , vol.48
    • Howe, R.1
  • 20
    • 0003322938 scopus 로고
    • Moduln mit einem höchsten Gewicht
    • Springer
    • J.C. Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Math., 750, Springer, 1979.
    • (1979) Lecture Notes in Math. , vol.750
    • Jantzen, J.C.1
  • 21
    • 0000647039 scopus 로고
    • Hermitean symmetric spaces and their unitary highest weight modules
    • H.P. Jakobsen, Hermitean symmetric spaces and their unitary highest weight modules, J. Funct. Anal., 52 (1983), 385-412.
    • (1983) J. Funct. Anal. , vol.52 , pp. 385-412
    • Jakobsen, H.P.1
  • 22
    • 0000295059 scopus 로고
    • Polar and Ol'shanskiǐ decompositions
    • J.D. Lawson, Polar and Ol'shanskiǐ decompositions, J. für Reine Ang. Math., 448 (1994), 191-219.
    • (1994) J. für Reine Ang. Math. , vol.448 , pp. 191-219
    • Lawson, J.D.1
  • 23
    • 0038840569 scopus 로고
    • Kähler coherent state orbits for representations of semisimple Lie groups
    • W. Lisiecki, Kähler coherent state orbits for representations of semisimple Lie groups, Ann. Inst. Henri Poincaré, 53(2) (1990), 245-258.
    • (1990) Ann. Inst. Henri Poincaré , vol.53 , Issue.2 , pp. 245-258
    • Lisiecki, W.1
  • 24
    • 84967708629 scopus 로고
    • A classification of coherent state representations of unimodular Lie groups
    • _, A classification of coherent state representations of unimodular Lie groups, Bull, of the AMS, 25(1) (1991), 37-43.
    • (1991) Bull, of the AMS , vol.25 , Issue.1 , pp. 37-43
  • 25
    • 84975974468 scopus 로고
    • On the fundamental group of a Lie semigroup
    • K.-H. Neeb, On the fundamental group of a Lie semigroup, Glasgow Math. J., 34 (1992), 379-394.
    • (1992) Glasgow Math. J. , vol.34 , pp. 379-394
    • Neeb, K.-H.1
  • 26
    • 0011615244 scopus 로고
    • Invariant subsemigroups of Lie groups
    • _, Invariant subsemigroups of Lie groups, Memoirs of the AMS, 499 (1993).
    • (1993) Memoirs of the AMS , vol.499
  • 28
    • 21844522122 scopus 로고
    • Contraction semigroups and representations
    • _, Contraction semigroups and representations, Forum Math., 6 (1994), 233-270.
    • (1994) Forum Math. , vol.6 , pp. 233-270
  • 29
    • 84972569081 scopus 로고
    • A convexity theorem for semisimple symmetric spaces
    • _, A convexity theorem for semisimple symmetric spaces, Pacific Journal of Math., 162(2) (1994), 305-349.
    • (1994) Pacific Journal of Math. , vol.162 , Issue.2 , pp. 305-349
  • 30
    • 51249170220 scopus 로고
    • On closedness and simple connectedness of adjoint and coadjoint orbits
    • _, On closedness and simple connectedness of adjoint and coadjoint orbits, Manuscripta Math., 82 (1994), 51-65.
    • (1994) Manuscripta Math. , vol.82 , pp. 51-65
  • 31
    • 0013548997 scopus 로고
    • Holomorphic representation theory I
    • _, Holomorphic representation theory I, Math. Annalen, 301 (1995), 155-181.
    • (1995) Math. Annalen , vol.301 , pp. 155-181
  • 32
    • 0000665109 scopus 로고
    • Holomorphic representation theory II
    • _, Holomorphic representation theory II, Acta Math., 173 (1994), 103-133.
    • (1994) Acta Math. , vol.173 , pp. 103-133
  • 33
    • 21844509656 scopus 로고
    • Kähler structures and convexity properties of coadjoint orbits
    • _, Kähler structures and convexity properties of coadjoint orbits, Forum Math., 7 (1995), 349-384.
    • (1995) Forum Math. , vol.7 , pp. 349-384
  • 34
    • 0002577660 scopus 로고
    • On the convexity of the moment mapping for a unitary highest weight representation
    • _, On the convexity of the moment mapping for a unitary highest weight representation, J. Funct. Anal., 127(2) (1995), 301-325.
    • (1995) J. Funct. Anal. , vol.127 , Issue.2 , pp. 301-325
  • 35
    • 0009085060 scopus 로고
    • Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series
    • G.I. Ol'shanskiǐ, Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series, Funct. Anal. and Appl., 15 (1982), 275-285.
    • (1982) Funct. Anal. and Appl. , vol.15 , pp. 275-285
    • Ol'shanskiǐ, G.I.1
  • 36
    • 0003564717 scopus 로고
    • Generalized coherent states and their applications
    • Springer
    • A. Perelomov, Generalized coherent states and their applications, Texts and Monographs in Physics, Springer, 1986.
    • (1986) Texts and Monographs in Physics
    • Perelomov, A.1
  • 37
    • 0010784430 scopus 로고
    • Unitary representations of a semi-direct product of Lie groups on ∂-cohomology spaces
    • I. Satake, Unitary representations of a semi-direct product of Lie groups on ∂-cohomology spaces, Math. Ann., 190 (1971), 177-202.
    • (1971) Math. Ann. , vol.190 , pp. 177-202
    • Satake, I.1
  • 38
    • 0001658382 scopus 로고
    • Analytic extension of the holomorphic discrete series
    • R.J. Stanton, Analytic Extension of the holomorphic discrete series, Amer. J. Math., 108 (1986), 1411-1424.
    • (1986) Amer. J. Math. , vol.108 , pp. 1411-1424
    • Stanton, R.J.1
  • 39
    • 0003893097 scopus 로고
    • Academic Press Inc., Boston, New York, Tokyo
    • N.R. Wallach, Real reductive groups I, Academic Press Inc., Boston, New York, Tokyo, 1988.
    • (1988) Real Reductive Groups I
    • Wallach, N.R.1
  • 40
    • 0003893097 scopus 로고
    • Academic Press Inc., Boston, New York, Tokyo
    • _, Real reductive groups II, Academic Press Inc., Boston, New York, Tokyo, 1992.
    • (1992) Real Reductive Groups II


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.