Multiline queues with spectral parameters
arXiv:1810.08157 · doi:10.1007/s00220-020-03694-4
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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