Purity of weakly separated set families

HwanChul Yoo (유환철)

School of Mathematics, KIAS, Seoul, Korea

School of Mathematics, KIAS, Seoul, Korea

2012/3/14 Wed 4PM-5PM

Weakly separated set families were first studied by Leclerc and Zelevinsky in the context of quantum flag variety. Two quantum Plücker coordinates quasi-commute whenever their indexing sets are weakly separated. It was conjectured that maximal such families always have the same size. Similar question was asked by Scott when she studied quantum Grassmannian. These conjectures were independently proved by Danilov-Karzanov-Koshevoy and Oh-Postnikov-Speyer using some planar graphs and by the author using truncation. In this talk, definitions and motivations for the weakly separated set families will be explained, including Oh-Postnikov-Speyer’s point of view on the subject. The proof of the purity conjecture using truncation will be provided, and related questions will be discussed.

Tags: 유환철