Eigenvalues and eigenstates of the s ell_q(2)-invariant Universal R-operator defined for cyclic representations at roots of unity

TL;DR

This paper constructs eigenstates and computes eigenvalues of the universal R-matrix for cyclic representations of the s ell_q(2) algebra at roots of unity, extending polynomial representations to theta-functions.

Contribution

It introduces a new framework for eigenstates of the universal R-matrix in cyclic representations at roots of unity, expanding beyond polynomial representations.

Findings

Eigenstates of the universal R-matrix are explicitly constructed.

Eigenvalues for these eigenstates are calculated.

Extension of polynomial representations to theta-functions at roots of unity.

Abstract

The s ell_q(2) representations are realized in the space of polynomials for general and exceptional values of deformation parameter q and on finite set of theta-functions for cyclic representation corresponding to q^N = +/- 1, which are a natural extension of the polynomials. The complete set of eigenstates of the Universal R-matrix are constructed and corresponding eigenvalues are calculated.