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DTSTART:20070311T020000
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DTSTAMP:20260903T145225
DTSTART;TZID=America/Detroit:20260911T150000
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SUMMARY:Workshop / Seminar:Type C multiline queues and the open-boundary TASEP
DESCRIPTION:The multispecies TASEP on a circle is a particle model whose partition function is connected to Macdonald polynomials at t=0. Multiline queues were introduced by Ferrari and Martin (2007) to compute the stationary distribution of the TASEP on a circle. Their construction admits a natural interpretation in terms of tensor products of Kirillov–Reshetikhin crystals of affine type A\, and a map from these tensor products to TASEP states is given by crystal-theoretic operations. We show that there is a natural Markov chain on the crystal that projects to the TASEP via this map.\nThe multispecies open boundary TASEP can be viewed as a type C analogue\, with its partition function connected to Koornwinder polynomials at t=0. However\, computing its stationary distribution beyond rank 1 has remained a longstanding open problem. Using Kirillov–Reshetikhin crystals of affine type C\, we construct type C multiline queues and a corresponding Ferrari–Martin pairing algorithm\, and show the crystal likewise admits a Markov chain that projects to the TASEP. Our construction is a combinatorial interpretation of the virtualization map for Kashiwara–Nakashima columns. We thus obtain a crystal-theoretic formula for the stationary distribution of the multispecies open boundary TASEP at the specialization alpha=beta=1. This is joint work with Jeronimo Valencia Porras.
UID:148388-21904175@events.umich.edu
URL:https://events.umich.edu/event/148388
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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