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

 

Double Vogan diagrams and semisimple symmetric spaces


Authors: Meng-Kiat Chuah and Jing-Song Huang
Journal: Trans. Amer. Math. Soc. 362 (2010), 1721-1750
MSC (2000): Primary 17B20, 53C35
Published electronically: November 18, 2009
MathSciNet review: 2574875
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Abstract: A Vogan diagram is a set of involution and painting on a Dynkin diagram. It selects a real form, or equivalently an involution, from a complex simple Lie algebra. We introduce the double Vogan diagram, which is two sets of Vogan diagrams superimposed on an affine Dynkin diagram. They correspond to pairs of commuting involutions on complex simple Lie algebras, and therefore provide an independent classification of the simple locally symmetric pairs.


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Additional Information

Meng-Kiat Chuah
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
Email: chuah@math.nthu.edu.tw

Jing-Song Huang
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Email: mahuang@ust.hk

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04895-8
PII: S 0002-9947(09)04895-8
Keywords: Vogan diagram, locally symmetric pair, Dynkin diagram, simple Lie algebra, involution
Received by editor(s): February 9, 2007
Published electronically: November 18, 2009
Additional Notes: The first author was supported in part by the National Center for Theoretical Sciences and the National Science Council of Taiwan.
The second author was supported in part by research grants from the Research Grant Council of HKSAR and the National Natural Science Foundation of China
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.