19 Citations
Inhomogeneous spin $q$-Whittaker polynomials
- Mathematics
- 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…
Representation theoretic interpretation and interpolation properties of inhomogeneous spin $q$-Whittaker polynomials
- Mathematics
- 2022
. We establish new properties of inhomogeneous spin q -Whittaker polynomials, which are symmetric polynomials generalizing t = 0 Macdonald polynomials. We show that these polynomials are defined in…
A Survey of $q$-Whittaker polynomials
- Mathematics
- 2020
Exploiting the fact that the $q$-Whittaker polynomials arise as a specialization of the (modified) Macdonald polynomials, we derive some of their basic properties, and explore interesting identities…
Modified Macdonald Polynomials and Integrability
- MathematicsCommunications in Mathematical Physics
- 2020
We derive combinatorial formulae for the modified Macdonald polynomial $$H_{\lambda }(x;q,t)$$ H λ ( x ; q , t ) using coloured paths on a square lattice with quasi-cylindrical boundary conditions.…
Nonsymmetric Macdonald polynomials via integrable vertex models
- MathematicsTransactions of the American Mathematical Society
- 2020
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…
Peter-Weyl, Howe and Schur-Weyl theorems for current groups
- Mathematics
- 2019
The classical Peter-Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in type A) this boils down to the Cauchy identity for…
Colored Fermionic Vertex Models and Symmetric Functions
- Mathematics
- 2021
In this text we introduce and analyze families of symmetric functions arising as partition functions for colored fermionic vertex models associated with the quantized affine Lie superalgebra Uq (…
Coloured stochastic vertex models and their spectral theory
- Mathematics
- 2018
This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following: …
Refined Cauchy identity for spin Hall-Littlewood symmetric rational functions
- MathematicsJ. Comb. Theory, Ser. A
- 2021
References
SHOWING 1-10 OF 36 REFERENCES
Whittaker functions on quantum groups and q-deformed Toda operators
- Mathematics
- 1999
In this paper we q-deform a construction of Kazhdan and Kostant from 1970's which produces quantum Toda Hamiltonians by considering the action of Casimirs of a simple Lie algebra on Whittaker…
A New Generalisation of Macdonald Polynomials
- Mathematics
- 2016
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate…
Stochastic higher spin six vertex model and Macdonald measures
- Mathematics
- 2016
We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional…
Cylindric Versions of Specialised Macdonald Functions and a Deformed Verlinde Algebra
- Mathematics
- 2013
We define cylindric versions of skew Macdonald functions Pλ/μ(q, t) for the special cases q = 0 or t = 0. Fixing two integers n > 2 and k > 0 we shift the skew diagram λ/μ, viewed as a subset of the…
Lectures on Integrable Probability: stochastic vertex models and symmetric functions
- Mathematics
- 2018
We consider a homogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and for the…
Pieri rules, vertex operators and Baxter Q-matrix
- Mathematics
- 2015
We use the Pieri rules to recover the q-boson model and show it is equivalent to a discretized version of the relativistic Toda chain. We identify its semi infinite transfer matrix and the…
Higher spin six vertex model and symmetric rational functions
- Mathematics
- 2016
We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and…
Coloured stochastic vertex models and their spectral theory
- Mathematics
- 2018
This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following: …