Decomposition of Affine Crystals in Levels 1 and 2

par Benedek Dombos (Université de Genève)

mardi 24 juin 2025, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux (ICJ, Université Lyon 1)

In this talk, I will discuss three classical infinite products arising from specializations of characters in type A_1^{(1)} at levels 1, 2, and 3. I will present new infinite sum expressions in levels 1 and 2, obtained by computing the major index statistic on Yamanouchi words. I will also present a new bijective proof at level 2 for the infinite sum expression found by Dousse, Hardiman and Konan, using perfect crystals. This is joint work with Jihyeug Jang.