# YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS

@article{Bufetov2019YANGBAXTERFF, title={YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS}, author={Alexey Bufetov and Leonid A. Petrov}, journal={Forum of Mathematics, Sigma}, year={2019}, volume={7} }

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…

## 17 Citations

Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field

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We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of the six vertex model…

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It is shown that for a certain class of initial conditions the point process associated with the dynamics has determinantal correlation functions, and the correlation kernel for one of the most classical initial conditions, the densely packed is calculated.

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The q-Whittaker function Wλ(x; q) associated to a partition λ is a q-analogue of the Schur function sλ(x), and is defined as the t = 0 specialization of the Macdonald polynomial Pλ(x; q, t). We give…

Spin q-Whittaker polynomials and deformed quantum Toda.

- Mathematics
- 2020

Spin $q$-Whittaker symmetric polynomials labeled by partitions $\lambda$ were recently introduced by Borodin and Wheeler (arXiv:1701.06292) in the context of integrable $\mathfrak{sl}_2$ vertex…

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We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That…

Some algebraic structures in the KPZ universality.

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We review some algebraic and combinatorial structures that underlie models in the KPZ universality class. Emphasis is given on the Robinson-Schensted-Knuth correspondence and its geometric lifting…

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