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Title: YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS
Employing bijectivization of summation identities, we introduce local stochastic moves based on the Yang–Baxter equation for $$U_{q}(\widehat{\mathfrak{sl}_{2}})$$ . Combining these moves leads to a new object which we call the spin Hall–Littlewood Yang–Baxter field—a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang–Baxter field with spin Hall–Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang–Baxter field leading to new dynamic versions of the stochastic six-vertex model and of the Asymmetric Simple Exclusion Process.  more » « less
Award ID(s):
1664617
PAR ID:
10156353
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Forum of Mathematics, Sigma
Volume:
7
ISSN:
2050-5094
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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