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arXiv · 2204.05935

The twist for Richardson varieties

Pavel Galashin·Thomas Lam
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Abstract

We construct the twist automorphism of open Richardson varieties inside the flag variety of a complex semisimple algebraic group. We show that the twist map preserves totally positive parts, and prove a Chamber Ansatz formula for it. Our twist map generalizes the twist maps previously constructed by Berenstein-Fomin-Zelevinsky, Marsh-Scott, and Muller-Speyer. We use it to explain the relationship between the two conjectural cluster structures for Richardson varieties studied by Leclerc and by Ingermanson.

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Pavel Galashin, Thomas Lam. 2022-04-12. The twist for Richardson varieties. https://arxiv.org/abs/2204.05935

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