Speaker: 高奕博教授，北京国际数学中心

Inviter: 聂思安

Title: Billey-Postnikov posets

Language: Chinese

Time & Venue: 2026.01.04 13:30-14:30 南楼N818

Abstract: Billey-Postnikov (BP) decompositions govern when Schubert varieties decompose as bundles of smaller Schubert varieties. In joint work with Christian Gaetz, we further develop the theory of BP decompositions and show that, in finite type, they can be recognized by pattern conditions and are indexed by the order ideals of a poset bp(w) that we introduce; we conjecture that this holds in any Coxeter group. We then apply BP decompositions to show that, when X(w) is rationally smooth and W simply laced, the Schubert structure constants under w satisfy a triangularity property, yielding a canonical involution on the Schubert cells of X(w) respecting Poincaré duality. We also classify the rationally smooth Bruhat intervals in finite type (other than E) which admit generalized Lehmer codes, answering questions and conjectures of Billey-Fan-Losonczy, Bolognini-Sentinelli, and Bishop-Milićević-Thomas. Time permitting, more implicit applications of BP decompositions will be discussed.