In 2021, Fang and Reineke described the support of linear degenerations of flag varieties in terms of Motzkin paths, by using Knight-Zelevinsky multi-segment duality. In a joint project with Esposito and Marietti we give a new characterization of supports in representation-theoretic terms by what we call excessive multi-segments. To do so we consider an algebraic structure on the set of Motzkin paths that we call Motzkin monoid. By using a universal property of the Motzkin monoid, we show that excessive multi segments are parametrized in a natural way by Motzkin paths. Moreover, we show that this parametrization coincides exactly with the Fang-Reineke parametrization. As a byproduct we have an elementary combinatorial criterion to decide if a multisegment is a support. We have an inductive procedure to describe the inverse of the Fang-Reineke map. In this term, there is a very beautiful (as yet conjectural) formula for the coefficients.
This talk relates to this arXiv paper.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
