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We study the stochastic colored six vertex (SC6V) model and its fusion. Ourmain result is an integral expression for natural observables of this model --joint q-moments of height functions. This generalises a recent result ofBorodin-Wheeler. The key technical ingredient is a new relation of heightfunctions of SC6V model in neighboring points. This relation is of independentinterest; we refer to it as a local relation. As applications, we give a newproof of certain symmetries of height functions of SC6V model recentlyestablished by Borodin-Gorin-Wheeler and Galashin, and new formulas for jointmoments of delayed partition functions of Beta polymer.

Observables of stochastic colored vertex models and local relation