Monodromy operators for higher rank

TL;DR

This paper derives explicit monodromy operators for the quantum group U_q(L(sl_3)) and provides formulas for quantum Casimir elements of U_q(gl_3) and U_q(sl_3), advancing understanding of quantum group structures.

Contribution

It presents explicit formulas for monodromy operators in higher rank quantum groups and new expressions for quantum Casimir elements, enhancing computational tools in quantum algebra.

Findings

Explicit form of monodromy operators for U_q(L(sl_3))

Formulas for quantum Casimir elements of U_q(gl_3) and U_q(sl_3)

Advances in quantum group representation theory

Abstract

We find the explicit form of the basic monodromy operators for the case of the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_3))$. Expressions for the quantum Casimir elements of the quantum groups $\mathrm U_q(\mathfrak{gl}_3)$ and $\mathrm U_q(\mathfrak{sl}_3)$ are obtained as a by-product.