The HHMP Decomposition of the Permutohedron and Degenerations of Torus Orbits in Flag Varieties
Year: 2024
Type: article
Abstract: Let $Z\subset \operatorname{Fl}(n)$ be the closure of a generic torus orbit in the full flag variety. Anderson–Tymoczko express the cohomology class of $Z$ as a sum of classes of Richardson varieties. Harada–Horiguchi–Masuda–Park give a decomposition of the permutohedron, the moment map image of $Z$, into subpolytopes corresponding to the summands of the Anderson–Tymoczko formula. We construct an explicit toric degeneration inside $\operatorname{Fl}(n)$ of $Z$ into Richardson varieties, whose moment map images coincide with the HHMP decomposition, thereby obtaining a new proof of the Anderson–Tymoczko formula.
DOI: 10.1093/imrn/rnae204
Author: Carl Lian
Institution: Tufts University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4402849579