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- Title
Mirkovic-Vilonen cycles and polytopes for a symmetric pair.
- 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.
- Subjects
POLYTOPES; MATHEMATICAL analysis; MATHEMATICAL formulas; MATHEMATICAL notation; ALGEBRA; MATHEMATICAL proofs
- Publication
Representation Theory, 2009, Vol 13, Issue 3, p19
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/S1088-4165-09-00341-0