Connection coefficients for 𝐴-type Jackson integral and Yang-Baxter equation

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

Advances in Difference Equations ◽

10.1186/s13662-021-03244-9 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Waleed M. Abd-Elhameed ◽

Youssri H. Youssri

Keyword(s):

Orthogonal Polynomials ◽

Chebyshev Polynomials ◽

Hypergeometric Functions ◽

Connection Coefficients ◽

Current Article ◽

In Virtue Of ◽

Connection Formulas

AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

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Trace and determinant in algebras associated with the yang-baxter equation

Functional Analysis and Its Applications ◽

10.1007/bf02577142 ◽

1987 ◽

Vol 21 (3) ◽

pp. 239-240

Author(s):

D. I. Gurevich

Keyword(s):

Baxter Equation

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Ore extensions of quasitriangular Hopf group coalgebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498814500169 ◽

2014 ◽

Vol 13 (06) ◽

pp. 1450016 ◽

Cited By ~ 1

Author(s):

Daowei Lu ◽

Dingguo Wang

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Baxter Equation ◽

Ore Extension ◽

Ore Extensions ◽

Necessary And Sufficient

In this paper, we mainly consider some special Ore extension of quasitriangular Hopf group coalgebra, and give the necessary and sufficient conditions when the Ore extension of quasitriangular Hopf group coalgebras will preserve the same quasitriangular structure. Furthermore, in the two examples given at the end, we construct new solutions of Yang–Baxter equation of Hopf group coalgebras version.

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