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Mirković-Vilonen cycles and polytopes for a symmetric pair

Author: Jiuzu Hong
Journal: Represent. Theory 13 (2009), 19-32
MSC (2000): Primary 20G05; Secondary 14M15
Published electronically: February 13, 2009
MathSciNet review: 2480386
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Abstract: Let $ G$ be a connected, simply-connected, and almost simple algebraic group, and let $ \sigma$ be a Dynkin automorphism on $ G$. Then $ (G,G^\sigma)$ is a symmetric pair. In this paper, we get a bijection between the set of $ \sigma$-invariant MV cycles (polytopes) for $ G$ and the set of MV cycles (polytopes) for $ G^\sigma$, which is the fixed point subgroup of $ G$; 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

Received by editor(s): May 13, 2008
Received by editor(s) in revised form: November 15, 2008
Published electronically: February 13, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.