The trigonometric $$E_8$$ R-matrix

Discrete Trigonometric Matrix Functions

We explore a pair of matrix solutions to a certain discrete system which has various properties similar to the familiar continuous trigonometric functions, including basic identities and sum and difference of two angles formulas. Then we examine separation properties of these matrices. An oscillation result is also given.

On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model

We elaborate the trigonometric version of intertwining vectors and factorized L-operators. The starting point is the corresponding elliptic construction with Belavin’s R-matrix. The naive trigonometric limit is singular and a careful analysis is needed. It is shown that the construction admits several different trigonometric degenerations. As a by-product, a quantum Lax operator for the trigono...

Modular transformation and twist between trigonometric limits of sl(n) elliptic R-matrix

We study the modular transformation of Zn-symmetric elliptic R-matrix and construct the twist between the trigonometric degeneracy of the elliptic R-matrix. Mathematics Subject Classifications (1991): 17B37, 81R10, 81R50, 16W30.

Controllability of Matrix Second Order Systems: a Trigonometric Matrix Approach

Many of the real life problems are modelled as Matrix Second Order Systems, (refer Wu and Duan [19], Hughes and Skelton [10]). Necessary and sufficient condition for controllability of Matrix Second Order Linear (MSOL) Systems has been established by Hughes and Skelton [10]. However, no scheme for computation of control was proposed. In this paper we first obtain another necessary and sufficien...

The partitioned R - matrix