Séminaire Lotharingien de Combinatoire, 95B.107 (2026), 12 pp.
Nantel Bergeron, Lucas Gagnon, Hunter Spink and Vasu Tewari
Introducing the Coxeter Flag Variety
Abstract.
Let W be a finite Weyl group and fix a Coxeter element c ∈ W.
We construct a complex of toric varieties in the complete flag variety
by setting all extremal generalized Plucker coordinates which are
not c-noncrossing to zero.
We describe the structure of this complex, including the corresponding
moment polytopes for each c, which reflect the structure
of c-clusters.
We give a GKM description of the (T-equivariant) cohomology
rings and show that its isomorphism type of this depends only on W.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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