On a conjecture about an analogue of Tokuyama’s theorem for $$G_2$$

Abstract

We prove the conjecture of Friedlander et al. (J Algebr Comb 41:1089, 2015) about sums over Littelmann patterns for the root system of type $$G_2$$ , which is an analogue of Tokuyama’s theorem Tokuyama (J Math Soc Jpn 40(4):671–685, 1988) for root systems of type $$A_r$$ . We use elementary means to show that the conjecture is implied by a finite set of polynomial identities.