Representations and identities of plactic-like monoids

We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids each finite rank as upper triangular matrices over any semiring from a large class including tropical fields characteristic 0. By analysing image these representations, we show that variety generated by single hypoplactic (respectively, stalactic or taiga) monoid at least 2 coincides with natural numbers together fixed H F) forms proper subvariety plactic 2.