Leaf posets and Hook Length Property

par Masao Ishikawa (Okayama University)

mardi 26 sept. 2017, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

R. Proctor gives a combinatorial definition of d-complete poset, which is a heap of a minuscule element of simply laced Kac-Moody Lie algebra. R. Proctor defined irreducibility of d-complete poset and classified d-complete posets into 15 irreducible classes. Dale Peterson and Proctor give the theorem that d-complete poset has hook-length property. We define leaf posets which generalize d-complete posets, and show that leaf posets has hook length property. We define 6 classes of basic leaf posets and show that the hook-length property reduces to certain Schur function identities which is also new.