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

DOI:
https://doi.org/10.1090/S1088-4165-09-00341-0

Published electronically:
February 13, 2009

MathSciNet review:
2480386

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Abstract | References | Similar Articles | Additional Information

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

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

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.