On the spectra of compact nilmanifolds
HTML articles powered by AMS MathViewer
- by Jeffrey S. Fox PDF
- Trans. Amer. Math. Soc. 290 (1985), 577-583 Request permission
Abstract:
We show the equivalence of the Howe-Richardson multiplicity formula for compact nilmanifolds and the formula obtained by Corwin and Greenleaf using the Selberg trace formula.References
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- Lawrence Corwin and Frederick P. Greenleaf, Character formulas and spectra of compact nilmanifolds, J. Functional Analysis 21 (1976), no. 2, 123–154. MR 0393345, DOI 10.1016/0022-1236(76)90074-4
- Jeffrey Fox, Frobenius reciprocity and extensions of nilpotent Lie groups, Trans. Amer. Math. Soc. 298 (1986), no. 1, 123–144. MR 857436, DOI 10.1090/S0002-9947-1986-0857436-1
- Roger Howe, On Frobenius reciprocity for unipotent algebraic groups over $Q$, Amer. J. Math. 93 (1971), 163–172. MR 281842, DOI 10.2307/2373455
- A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
- A. I. Malcev, On a class of homogeneous spaces, Amer. Math. Soc. Translation 1951 (1951), no. 39, 33. MR 0039734
- Calvin C. Moore, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups, Ann. of Math. (2) 82 (1965), 146–182. MR 181701, DOI 10.2307/1970567
- Richard Penney, Abstract Plancherel theorems and a Frobenius reciprocity theorem, J. Functional Analysis 18 (1975), 177–190. MR 0444844, DOI 10.1016/0022-1236(75)90023-3
- Lawrence Corwin, Frederick P. Greenleaf, and Richard Penney, A general character formula for irreducible projections on $L^{2}$ of a nilmanifold, Math. Ann. 225 (1977), no. 1, 21–32. MR 425021, DOI 10.1007/BF01364889
- Leonard F. Richardson, Decomposition of the $L^{2}$-space of a general compact nilmanifold, Amer. J. Math. 93 (1971), 173–190. MR 284546, DOI 10.2307/2373456
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 290 (1985), 577-583
- MSC: Primary 22E27
- DOI: https://doi.org/10.1090/S0002-9947-1985-0792812-6
- MathSciNet review: 792812