# The duality correspondence of infinitesimal characters

Colloquium Mathematicae (1996)

- Volume: 70, Issue: 1, page 93-102
- ISSN: 0010-1354

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topPrzebinda, Tomasz. "The duality correspondence of infinitesimal characters." Colloquium Mathematicae 70.1 (1996): 93-102. <http://eudml.org/doc/210401>.

@article{Przebinda1996,

abstract = {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.},

author = {Przebinda, Tomasz},

journal = {Colloquium Mathematicae},

keywords = {infinitesimal characters; representations; Howe's duality theorem; dual pairs},

language = {eng},

number = {1},

pages = {93-102},

title = {The duality correspondence of infinitesimal characters},

url = {http://eudml.org/doc/210401},

volume = {70},

year = {1996},

}

TY - JOUR

AU - Przebinda, Tomasz

TI - The duality correspondence of infinitesimal characters

JO - Colloquium Mathematicae

PY - 1996

VL - 70

IS - 1

SP - 93

EP - 102

AB - 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.

LA - eng

KW - infinitesimal characters; representations; Howe's duality theorem; dual pairs

UR - http://eudml.org/doc/210401

ER -

## References

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- [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. Zbl0558.22018
- [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. Zbl0254.17004
- [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. Zbl0375.22009
- [16] A. Knapp, Representation Theory of Semisimple Groups - an Overview Based on Examples, Princeton University Press, Princeton, N.J., 1986. Zbl0604.22001
- [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. Zbl0434.22011
- [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. Zbl1024.20502

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