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Mirković-Vilonen cycles and polytopes for a symmetric pair
Author(s):
Jiuzu
Hong
Journal:
Represent. Theory
13
(2009),
19-32.
MSC (2000):
Primary 20G05;
Secondary 14M15
Posted:
February 13, 2009
MathSciNet review:
2480386
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Additional information
Abstract:
Let  be a connected, simply-connected, and almost simple algebraic group, and let  be a Dynkin automorphism on  . Then  is a symmetric pair. In this paper, we get a bijection between the set of  -invariant MV cycles (polytopes) for  and the set of MV cycles (polytopes) for  , which is the fixed point subgroup of  ; moreover, this bijection can be restricted to the set of MV cycles (polytopes) in irreducible representations. As an application, we obtain a new proof of the twining character formula.
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Additional Information:
Jiuzu
Hong
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Address at time of publication:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
Email:
hjzzjh@gmail.com
DOI:
10.1090/S1088-4165-09-00341-0
PII:
S 1088-4165(09)00341-0
Received by editor(s):
May 13, 2008
Received by editor(s) in revised form:
November 15, 2008
Posted:
February 13, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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