On the fundamental group of open Richardson varieties

Changzheng Li; Frank Sottile; Chi Zhang

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arXiv · 1911.11748

On the fundamental group of open Richardson varieties

Changzheng Li·Frank Sottile·Chi Zhang

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Abstract

We compute the fundamental group of an open Richardson variety in the manifold of complete flags that corresponds to a partial flag manifold. Rietsch showed that these log Calabi-Yau varieties underlie a Landau-Ginzburg mirror for the Langlands dual partial flag manifold, and our computation verifies a prediction of Hori for this mirror. It is log Calabi-Yau as it isomorphic to the complement of the Knutson-Lam-Speyer anti-canonical divisor for the partial flag manifold. We also determine explicit defining equations for this divisor.

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Changzheng Li, Frank Sottile, Chi Zhang. 2019-11-26. On the fundamental group of open Richardson varieties. https://arxiv.org/abs/1911.11748

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