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arXiv · 0711.0070

Mirkovic-Vilonen cycles and polytopes for a Symmetric pair

Jiuzu Hong
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Abstract

Let $G$ be a connected, simply-connected, and almost simple algebraic group, and let $σ$ be a Dynkin automorphism on $G$. In this paper, we get a bijection between the set of $\st$-invariant MV cycles (polytopes) for $G$ and the set of MV cycles (polytopes) for $G^\st$, 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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BibTeXRIS

Jiuzu Hong. 2008-11-15. Mirkovic-Vilonen cycles and polytopes for a Symmetric pair. https://doi.org/10.1090/s1088-4165-09-00341-0

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