Séminaire Lotharingien de Combinatoire, 89B.52 (2023), 12 pp.
Edward Richmond, Mihail Ţarigradschi and Weihong Xu
The Isomorphism Problem for Cominuscule Schubert Varieties
Abstract.
Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These labeled posets generalize Young diagrams. We prove that Schubert varieties in potentially different cominuscule flag varieties are isomorphic as varieties if and only if their corresponding labeled posets are isomorphic, generalizing the classification of Grassmannian Schubert varieties using Young diagrams by the last two authors. Our proof is type-independent.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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