Osaka Journal of Mathematics

On the Benson-Ratcliff invariant of coadjoint orbits on nilpotent Lie groups

Ali Baklouti and Khaled Tounsi

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Abstract

We provide in this paper a counterexample to the Benson-Ratcliff conjecture about a cohomology class invariant on coadjoint orbits on nilpotent Lie groups. We prove that this invariant never vanishes on generic coadjoint orbits for some restrictive classes. As such, it does separate up to invariant factor, unitary representations associated to generic orbits in some cases.

Article information

Source
Osaka J. Math. Volume 44, Number 2 (2007), 399-414.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1183667987

Mathematical Reviews number (MathSciNet)
MR2351008

Zentralblatt MATH identifier
1143.22007

Subjects
Primary: 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) 22D10: Unitary representations of locally compact groups

Citation

Baklouti, Ali; Tounsi, Khaled. On the Benson-Ratcliff invariant of coadjoint orbits on nilpotent Lie groups. Osaka J. Math. 44 (2007), no. 2, 399--414.https://projecteuclid.org/euclid.ojm/1183667987


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References

  • A. Baklouti and N. Ben Salah: The $L^p$-$L^q$ version of Hardy's theorem on nilpotent Lie groups, Forum Math. 18 (2006), 245--262.
  • A. Baklouti, N. Ben Salah and K. Smaoui: Some uncertainty principles on nilpotent Lie groups; in Banach Algebras and Their Applications, Contemp. Math. 363, Amer. Math. Soc., Providence, RI, 2004, 39--52.
  • A. Baklouti, C. Benson and G. Ratcliff: Moment sets and the unitary dual of a nilpotent Lie group, J. Lie Theory 11 (2001), 135--154.
  • C. Benson and G. Ratcliff: An invariant for unitary representations of nilpotent Lie groups, Michigan Math. J. 34 (1987), 23--30.
  • C. Benson and G. Ratcliff: Quantization and invariant for unitary representation of nilpotent Lie groups, Illinois J. Math. 32 (1988), 53--64.
  • L.J. Corwin and F.P. Greenleaf: Representations of Nilpotent Lie Groups and Their Applications. Part 1: Basic Theory and Examples, Cambridge Univ. Press, Cambridge, 1990.
  • R. Goodman and N. Wallach: Representations and Invariants of the Classical Groups, Encyclopedia of Mathematics and its Applications 68, Cambridge Univ. Press, Cambridge, 1998.
  • H. Leptin and J. Ludwig: Unitary Representation Theory of Exponential Lie Groups, de Gruyter Expositions in Mathematics 18, Walter de Gruyter & Co., Berlin, 1994.