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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Primitive spherical systems


Author: P. Bravi
Journal: Trans. Amer. Math. Soc. 365 (2013), 361-407
MSC (2010): Primary 14M27; Secondary 05E10, 05E15
Published electronically: August 10, 2012
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Abstract: A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (such as parabolic induction and wonderful fiber product) from the so-called primitive spherical systems. Here we classify the primitive spherical systems. As an application, we prove that the quotients of a spherical system are in correspondence with the so-called distinguished subsets of colors.


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Additional Information

P. Bravi
Affiliation: Dipartimento di Matematica, Università La Sapienza, P.le A. Moro 5, 00185 Roma, Italy
Email: bravi@mat.uniroma1.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05621-2
PII: S 0002-9947(2012)05621-2
Keywords: Wonderful varieties, root systems.
Received by editor(s): July 19, 2010
Received by editor(s) in revised form: January 21, 2011, and April 4, 2011
Published electronically: August 10, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.