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 $G$. 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.

12 pages; This is a shortened version

References in corpus (3)

• Perverse sheaves on a Loop group and Langlands' duality
• Mirkovic-Vilonen cycles and polytopes
• On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian

Cited by in corpus (3)

• Tensor invariants, Saturation problems, and Dynkin automorphisms
• Conformal blocks, Verlinde formula and diagram automorphisms
• Dynkin automorphism actions on Gaudin algebras