Séminaire Lotharingien de Combinatoire, 91B.95 (2024), 12 pp.
Jonah Berggren and Jonathan Boretsky
Combinatorics of Boundary Algebras
Abstract.
Boundary algebras are an important tool in the categorification, by Jensen, King and Su and by Pressland, of cluster structures on positroid varieties, defined by Scott and by Galashin and Lam. Each connected positroid has a corresponding boundary algebra. We give a combinatorial way to recover a positroid from its boundary algebra. We then describe the set of algebras which arise as the boundary algebra of some positroid. Finally, we give the first complete description of the minimal relations in the boundary algebra. We expect this description to be helpful in extending results known for Grassmannian boundary algebras to more general settings.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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