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1996 | 70 | 1 | 93-102
Tytuł artykułu

The duality correspondence of infinitesimal characters

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.
Słowa kluczowe
Rocznik
Tom
70
Numer
1
Strony
93-102
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-05-17
Twórcy
  • Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, U.S.A.
Bibliografia
  • [1] J. D. Adams, Discrete spectrum of the reductive dual pair (O(p,q), Sp(2m)), Invent. Math. 74 (1983), 449-475.
  • [2] J. D. Adams, Unitary highest weight modules, preprint.
  • [3] N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris, 1968.
  • [4] T. Y. Enright, R. Howe and N. R. Wallach, A classification of unitary highest weight modules, in: Representation Theory of Reductive Groups, P. C. Trombi (ed.), Birkhäuser, Boston, 1983, 97-143.
  • [5] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962.
  • [6] R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989), 539-570.
  • [7] R. Howe, Transcending the classical invariant theory, J. Amer. Math. Soc. 74 (1989), 449-475.
  • [8] R. Howe, θ-series and invariant theory, in: Proc. Sympos. Pure Math. 33, Amer. Math. Soc., Providence, R.I., 1979, 275-285.
  • [9] R. Howe, manuscript in preparation on dual pairs.
  • [10] R. Howe, Dual pairs in physics: harmonic oscillators, photons, electrons, and singletons, in: Lectures in Appl. Math. 21, Amer. Math. Soc., Providence, R.I., 1985, 179-207.
  • [11] R. Howe, On a notion of rank for unitary representations of the classical groups, in: Harmonic Analysis and Group Representations, Liguori, Napoli, 1982, 223-331.
  • [12] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, Berlin, 1972.
  • [13] N. Jacobson, Basic Algebra I, W. H. Freeman, 1974.
  • [14] N. Jacobson, Basic Algebra II, W. H. Freeman, 1980.
  • [15] M. Kashiwara and M. Vergne, On the Segal-Shale-Weil representation and harmonic polynomials, Invent. Math. 44 (1978), 1-97.
  • [16] A. Knapp, Representation Theory of Semisimple Groups - an Overview Based on Examples, Princeton University Press, Princeton, N.J., 1986.
  • [17] A. Knapp and D. Vogan, Jr., Duality theorems in the relative Lie algebra cohomology, preprint.
  • [18] R. Parthasarathy, Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci. 89 (1980), 1-24.
  • [19] D. Vogan, Jr., Representation Theory of Real Reductive Lie Groups, Birkhäuser, Boston, 1981.
  • [20] D. Vogan, Classifying representations by lowest K-types, in: Lectures in Appl. Math. 21, Amer. Math. Soc., 1985, 179-207.
  • [21] H. Weyl, The Classical Groups, Princeton University Press, Princeton, N.J., 1946.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv70i1p93bwm
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