Meromorphicity of spectral universal K-matrices

Show that, for every finite-dimensional type-1 Uq(g′)-module V and for generic QSP parameters, the spectral universal K-matrix Kv(z) is the Laurent series expansion of a meromorphic End(V)-valued function of the spectral parameter z.

Background

Spectral K-matrices K(z) arise from cylindrical structures combined with grading shifts and satisfy generalized spectral reflection equations. For irreducible modules, these yield trigonometric K-matrices; for general modules, the spectral K-matrix is defined as a formal Laurent series.

The conjecture parallels known meromorphicity results for spectral R-matrices, asserting that the formal expansions Kv(z) come from genuine meromorphic functions, which is essential for analytic and representation-theoretic applications.