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On the $ p$-compact groups corresponding to the $ p$-adic reflection groups $ G(q,r,n)$

Author(s): Natàlia Castellana
Journal: Trans. Amer. Math. Soc. 358 (2006), 2799-2819.
MSC (2000): Primary 55R35, 14E20; Secondary 55R40, 20D20
Posted: February 6, 2006
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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.

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Additional Information:

Natàlia Castellana
Affiliation: Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bellaterra, Spain

DOI: 10.1090/S0002-9947-06-04154-7
PII: S 0002-9947(06)04154-7
Keywords: Classifying space, $p$-compact group, spherical fibration
Received by editor(s): January 14, 2002
Posted: February 6, 2006
Additional Notes: The author was supported by CIRIT Grant 1995FI-02105PG and by MCYT grant BFM 2001-2035.
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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