Higher spin six vertex model and symmetric rational functions

Borodin, Alexei; Petrov, Leonid

doi:10.1007/s00029-016-0301-7

Cited by 124 publications

(315 citation statements)

References 72 publications

Supporting

Mentioning

304

Contrasting

Order By: Relevance

“…In (1.1), the stochastic R-matrices depend on a number of parameters, by specializing which one can degenerate the Higher Spin Six Vertex Model to previously mentioned models including the q-TASEP, the q-Hahn TASEP or the ASEP. In [18] a description of the Higher Spin Six Vertex Model complementary to that of [26] was offered using a language closer to that of the Schur processes. Here, the model was studied through a family of symmetric rational functions whose properties descended from the commutation relation (1.1) and that are in fact multi-parameter generalizations of the Schur functions.…”

Section: Introductionmentioning

confidence: 99%

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

Imamura

Mucciconi

Sasamoto

2020

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

In this paper we consider the Higher Spin Six Vertex Model on the lattice Z ≥2 × Z ≥1 . We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions. Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model. In particular, along the characteristic line we recover Baik-Rains fluctuations with size of characteristic exponent 1/3. We also consider some of the main degenerations of the Higher Spin Six Vertex Model and we adapt our analysis to the relevant cases of the q-Hahn particle process and of the Exponential Jump Model.

show abstract

Section: Introductionmentioning

confidence: 99%

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

Imamura

Mucciconi

Sasamoto

2020

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

show abstract

“…The asymmetric simple exclusion process (ASEP) [5] is one of the most studied examples, both on a line and with open boundary conditions (see, for example, [6][7][8][9]). It is intimately connected to the higher spin stochastic six vertex model which has been studied on a quadrant or a semi-infinite line with simple open boundary conditions [10][11][12]. The R-matrix of the higher spin six vertex model is related to the higher weight representations of the U q ( sl(2)) algebra and the explicit formula was derived in [13].…”

Section: Introductionmentioning

confidence: 99%

Boundary matrices for the higher spin six vertex model

Mangazeev

2019

Nuclear Physics B

View full text Add to dashboard Cite

In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin R-matrix is associated with the affine quantum algebra U q ( sl(2)). The explicit formulas for boundary K-matrices for spins s = 1/2, 1 are well known. We derive difference equations for the generating function of matrix elements of the K-matrix for any spin s and solve them in terms of hypergeometric functions. As a result we derive the explicit formula for matrix elements of the K-matrix for arbitrary spin. In the lower-and upper-triangular cases, the K-matrix simplifies and reduces to simple products of q-Pochhammer symbols.then we obtain K J (y) J J = 1 by using the definition (3.13) of the Φ function. Applying the q-Vandermonde summation formula (A.7) it is easy to check that J j=0 K J (y) l j = 1, (5.5) J j=0 K J (y) l j = J l=0(−vt) l (q −2J ; q 2 ) l (q 2 ; q 2 ) l = (−vtq −2J ; q 2 ) J , (7.19)

show abstract

“…Previously a closed formula for the higherspin R-matrix of the 6-vertex model was obtained in [19] based on the positive solution of the tetrahedron equation [18]. It can be interpreted as the R-matrix of the higher-spin stochastic 6-vertex model [20][21][22][23]. Under a special choice of the spectral parameter [21] this model degenerates into the q-Hahn system which corresponds to the most general "chipping model" introduced by Povolotsky [24].…”

Section: Introductionmentioning

confidence: 99%

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Bosnjak¹,

Mangazeev²

2016

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this paper we construct a new factorized representation of the R-matrix related to the affine algebra U q ( sl n ) for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the R-matrix and give a simple proof that a "twisted" R-matrix is stochastic. We also discuss symmetries of the R-matrix, its degenerations and compare our formulas with other results available in the literature.

show abstract

Higher spin six vertex model and symmetric rational functions

Cited by 124 publications

References 72 publications

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

Boundary matrices for the higher spin six vertex model

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Contact Info

Product

Resources

About