Communications in Number Theory and Physics
Volume 17 (2023)
On the fundamental group of open Richardson varieties
Pages: 77 – 101
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.
flag variety, open Richardson variety, fundamental group, mirror symmetry
2010 Mathematics Subject Classification
Primary 14J33, 14M15. Secondary 57M05.
C. Li is supported by NSFC Grants 11831017, 11822113, and 11771455.
F. Sottile is supported by grant 636314 from the Simons Foundation.
Received 20 August 2020
Accepted 1 October 2022
Published 23 February 2023