Weyl group extension of quantized current algebras

TL;DR

This paper extends the Drinfeld current realization of quantum affine algebras and Yangians by constructing current operators for non-simple roots, defining a new braid group action, and describing the universal R-matrix in novel forms.

Contribution

It introduces a new extension of the Drinfeld current realization, including non-simple roots and a new braid group action, along with explicit R-matrix descriptions.

Findings

Constructed current operators for non-simple roots.

Defined a new braid group action in terms of current operators.

Described the universal R-matrix as an infinite product and integrals.

Abstract

In this paper, we extend the Drinfeld current realization of quantum affine algebras $U_q(\hat {\gg})$ and of the Yangians in several directions: we construct current operators for non-simple roots of ${\gg}$, define a new braid group action in terms of the current operators and describe the universal R-matrix for the corresponding ``Drinfeld'' comultiplication in the form of infinite product and in the form of certain integrals over current operators.