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Séminaire Combinatoire et Théorie des Nombres ICJ

# Leaf posets and Hook Length Property

## by Masao Ishikawa (Okayama University)

mardi 26 septembre 2017 de au (Europe/Paris)
at ICJ, Université Lyon 1 ( Bât. Braconnier, salle Fokko du Cloux )
 Description 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.