On Demazure crystals for $U_{q}(G_{2}^{(1)})$

Abstract

Abstract. We show that there exist suitable sequences {w (k) } k≥0 and {w (k) } k≥0 of Weyl group elements for a given perfect crystal of level l ≥ 1 such that the path realizations of the Demazure crystals B w (k) (lΛ 0 ) and2 ) have tensor-product-like structures with mixing index κ = 1.