Quantum R-matrix and Intertwiners for the Kashiwara Algebra

TL;DR

This paper explores the structure of the Kashiwara algebra, introducing intertwiners and demonstrating their connection to quantum R-matrices, along with establishing their commutation relations and an analogue of the universal R-matrix.

Contribution

It introduces intertwiners for the Kashiwara algebra and links them to quantum R-matrices, providing new insights into their algebraic relations and structures.

Findings

Matrix from 2-point functions matches quantum R-matrix (up to diagonal)

Established commutation relations of intertwiners

Introduced an analogue of the universal R-matrix for Kashiwara algebra

Abstract

We study the algebra $B_q(\ge)$ presented by Kashiwara and introduce intertwiners similar to $q$-vertex operators. We show that a matrix determined by 2-point functions of the intertwiners coincides with a quantum R-matrix (up to a diagonal matrix) and give the commutation relations of the intertwiners. We also introduce an analogue of the universal R-matrix for the Kashiwara algebra.