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abstract: 'We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence of a quantum group anomalous term which vanishes in the classical case. This is called [*the quantum group anomaly*]{}. We derive the new qRG equations for the XXZ model and show that the RG-flow diagram obtained in this fashion exhibits the correct line of critical points that the exact model has. In the ITF model the qRG-flow equations coincide with the tensor product decomposition of cyclic irreps of $SU_q(2)$ with $q^4=1$.'
author:
- |
    [**Miguel A. Martín-Delgado**]{} and [**Germán Sierra**]{}\
    \
    \
    [*Universidad Complutense. 28040-Madrid, Spain* ]{}\
    \
    [*Serrano 123, 28006-Madrid, Spain* ]{}
title: |
     [**The Renormalization Group Method\
    and Quantum Groups:**]{}\
    [**the postman always rings twice** ]{}[^1] 
---

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