On the $p$-compact groups corresponding to the $p$-adic reflection groups $G(q,r,n)$
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Abstract:
There exists an infinite family of $p$-compact groups whose Weyl groups correspond to the finite $p$-adic pseudoreflection groups $G(q,r,n)$ of family 2a in the Clark-Ewing list. In this paper we study these $p$-compact groups. In particular, we construct an analog of the classical Whitney sum map, a family of monomorphisms and a spherical fibration which produces an analog of the classical $J$-homomorphism. Finally, we also describe a faithful complexification homomorphism from these $p$-compact groups to the $p$-completion of unitary compact Lie groups.References
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Additional Information
- Natàlia Castellana
- Affiliation: Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bella- terra, Spain
- Received by editor(s): January 14, 2002
- Published electronically: February 6, 2006
- Additional Notes: The author was supported by CIRIT Grant 1995FI-02105PG and by MCYT grant BFM 2001-2035.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 2799-2819
- MSC (2000): Primary 55R35, 14E20; Secondary 55R40, 20D20
- DOI: https://doi.org/10.1090/S0002-9947-06-04154-7
- MathSciNet review: 2216246