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Coming event(s)


  • Tuesday, 27th November, 2018

    Title: Multiline Queues With Spectral Parameters
    Speaker: Dr Travis Scrimshaw, School of Mathematics and Physics, University of Queensland, Australia
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The (multispecies) Totally Asymmetric Simple Exclusion Process (TASEP) is a Markov chain on a 1D lattice that can be used to model cars moving through traffic. When we consider this process on a ring, a solution for the steady-state distribution was given by Ferrari and Martin using multiline queues (MLQs), a sequence of subsets of {1,2,...,n}, which are called queues. By generalizing MLQs to functions on words the commutativity conjecture of Arita et al. roughly says that for a fixed word u and set of sizes, the number of MLQs that result in u when applied to the word 11...1 does not depend on the order chosen for the sizes of the queues. In this talk, we refine this conjecture by putting a weighting on MLQs, which we call spectral parameters, and show that with this weighting, the resulting sum does not depend on the order chosen. Our proof uses the relation between MLQs, tensor products of Kirillov-Reshetikhin crystals, and (combinatorial) R-matrices using a corner transfer matrix given by Kuniba, Maruyama, and Okado. This is joint work with Erik Aas and Darij Grinberg.