Yang-Baxter representations of the infinite symmetric group

The Strongly Symmetric Elements and Solutions of Yang-baxter Equation

It is shown that all strongly symmetric elements are solutions of constant classical Yang-Baxter equation in Lie algebra, or of quantum Yang-Baxter equation in algebra. Otherwise, all solutions of constant classical Yang-Baxter equation (CYBE) in Lie algebra L with dim L ≤ 3 over field k of characteristic 2 are obtained 0 Introduction The Yang-Baxter equation first came up in a paper by Yang as...

The Yang-Baxter equation, symmetric functions, and Schubert polynomials

We present an approach to the theory of Schubert polynomials, corresponding symmetric functions, and their generalizations that is based on exponential solutions of the Yang-Baxter equation. In the case of the solution related to the nilCoxeter algebra of the symmetric group, we recover the Schubert polynomials of Lascoux and Schiitzenberger, and provide simplified proofs of their basic propert...

Infinite Hopf Families of Algebras and Yang-Baxter Relations

A Yang-Baxter relation-based formalism for generalized quantum affine algebras with the structure of an infinite Hopf family of (super-) algebras is proposed. The structure of the infinite Hopf family is given explicitly on the level of L matrices. The relation with the Drinfeld current realization is established in the case of 4 × 4 R-matrices by studying the analogue of the Ding-Frenkel theor...

Quantum Group Representations and Baxter Equation

In this article we propose algebraic universal procedure for deriving ”fusion rules” and Baxter equation for any integrable model with Uq(ŝl2) symmetry of Quantum Inverse Scattering Method. Baxter Qoperator is got from the certain infinite dimensional representation of the Universal Rmatrix for Uq(ŝl2) affine algebra. The algebraic properties of Q-operator are examined.

Infinite-dimensional Group Representations