Multiline queues with spectral parameters

Abstract

Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show that the spectral weight of a word is invariant under a natural action of the symmetric group, giving a proof of the commutativity conjecture of Arita, Ayyer, Mallick, and Prolhac. We give a determinant formula for the spectral weight of a word, which gives a proof of a conjecture of the first author and Linusson.

44 pages, 6 figures; see the ancillary file for a long version

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• Asymptotics in ASEP with Step Initial Condition
• Matrix representation of the stationary measure for the multispecies TASEP
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Spurious phase in a model for traffic on a bridge
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Cited by in corpus (3)

• KPZ fluctuations in finite volume
• Quasi-solvable lattice models for ${\mathrm{Sp}}_{2n}$ and ${\mathrm{SO}}_{2n+1}$ Demazure atoms and characters
• Twisted multiline queues for the steady states of TASEP and TAZRP