## Mirković-Vilonen cycles and polytopes for a symmetric pair

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- by Jiuzu Hong PDF
- Represent. Theory
**13**(2009), 19-32 Request permission

## 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.## References

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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
- MR Author ID: 862719
- Email: hjzzjh@gmail.com
- Received by editor(s): May 13, 2008
- Received by editor(s) in revised form: November 15, 2008
- Published electronically: February 13, 2009
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**13**(2009), 19-32 - MSC (2000): Primary 20G05; Secondary 14M15
- DOI: https://doi.org/10.1090/S1088-4165-09-00341-0
- MathSciNet review: 2480386