• Corpus ID: 233025280

Inhomogeneous spin $q$-Whittaker polynomials

@inproceedings{Borodin2021InhomogeneousS,
  title={Inhomogeneous spin \$q\$-Whittaker polynomials},
  author={Alexei Borodin and Sergei Korotkikh},
  year={2021}
}
We introduce and study an inhomogeneous generalization of the spin q-Whittaker polynomials from [BW17]. These are symmetric polynomials, and we prove a branching rule, skew dual and non-dual Cauchy identities, and an integral representation for them. Our main tool is a novel family of deformed Yang-Baxter equations. 
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References

SHOWING 1-10 OF 41 REFERENCES

Observables of Stochastic Colored Vertex Models and Local Relation

We study the stochastic colored six vertex (SC6V) model and its fusion. Our main result is an integral expression for natural observables of this model -- joint q-moments of height functions. This

Double Grothendieck Polynomials and Colored Lattice Models

We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe dreams and recent

Spin q-Whittaker polynomials and deformed quantum Toda.

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

Observables of coloured stochastic vertex models and their polymer limits

In the context of the coloured stochastic vertex model in a quadrant, we identify a family of observables whose averages are given by explicit contour integrals. The observables are certain linear

Shift‐invariance for vertex models and polymers

We establish a symmetry in a variety of integrable stochastic systems: certain multi‐point distributions of natural observables are unchanged under a shift of a subset of observation points. The

A short proof of macdonald's conjecture for the root systems of type a

We give a new proof of I. G. Macdonald's conjecture for the root systems of type A (or equivalently, the equal parameter q-Dyson Theorem) that is short, elementary and direct. We also give a short

Nonsymmetric Macdonald polynomials via integrable vertex models

Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$. Using the Yang-Baxter algebra of the

Yang-Baxter equation, symmetric functions and Grothendieck polynomials

New development of the theory of Grothendieck polynomials, based on an exponential solution of the Yang-Baxter equation in the algebra of projectors are given.