Canonical objects in Kirillov theory on nilpotent Lie groups
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- by Richard C. Penney PDF
- Proc. Amer. Math. Soc. 66 (1977), 175-178 Request permission
Abstract:
It is shown that to each element f in the dual space of the Lie algebra of a nilpotent Lie group there is a uniquely defined subgroup ${K_\infty }$ for which the representation corresponding to f is inducible from a square-integrable-modulo-its-kernel representation of ${K_\infty }$.References
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P. Bernat et al., Represéntations des groupes de Lie résolubles, Dunod, Paris, 1972.
L. Corwin, F. Greenleaf and R. Penney, A general character formula for the irreducible projections on ${L^2}$ of a nilmanifold (preprint).
- G. W. Mackey, The theory of group representations. Three volumes, University of Chicago, Department of Mathematics, Chicago, Ill., 1955. Lecture notes (Summer, 1955) prepared by Dr. Fell and Dr. Lowdenslager. MR 0086063
- Calvin C. Moore and Joseph A. Wolf, Square integrable representations of nilpotent groups, Trans. Amer. Math. Soc. 185 (1973), 445–462 (1974). MR 338267, DOI 10.1090/S0002-9947-1973-0338267-9
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 175-178
- MSC: Primary 22E25; Secondary 22E45, 43A80
- DOI: https://doi.org/10.1090/S0002-9939-1977-0453922-7
- MathSciNet review: 0453922