Twisted multiline queues for the steady states of TASEP and TAZRP

We define a new algorithm on fermionic and bosonic twisted multiline queues that projects to the multispecies totally asymmetric simple exclusion process (TASEP) and the totally asymmetric zero range process (TAZRP) on a ring, respectively. Our algorithm on fermionic multiline queues generalizes the Ferrari–Martin algorithm for TASEP, and we show it is equivalent to the algorithm of Arita–Ayyer–Mallick–Prolhac (2011). Meanwhile, our algorithm on bosonic multiline queues is a novel generalization of the corresponding algorithm of Kuniba–Maruyama–Okado (2016) for the TAZRP. Additionally, we define a new Markov process on bosonic twisted multiline queues that projects to the TAZRP and intertwines with the symmetric group action on the rows of the multiline queues.