The network comprises eight primary sites, six in Europe and two in Israel listed below. It has several secondary sites as indicated in the Plan of the Network.
| Local coordinator: | H.H. Andersen, mathha@mi.aau.dk | 
| Research domains: | Representation theory of  Lie algebras Linear algebraic groups and Quantum groups Characteristic p methods in algebraic geometry | 
| Satellites: | University of Copenhagen | 
| Local coordinator: | F. Van Oystaeyen, francin@wins.uia.ac.be | 
| Research domains: | Noncommutative geometry Artin algebras Valuation theory Hopf algebras Invariant theory Differential operator algebras | 
| Satellites: | Rijksuniversitair Centrum Antwerpen University of Glasgow King's College London Vrije University of Brussels University of Leiden University of Limburg | 
| Local coordinator: | C.M. Ringel, ringel@mathematik.uni-bielefeld.de | 
| Research domains: | Quiver varieties Quantum groups Quasi-hereditary algebras Canonical Bases | 
| Satellites: | University of Hamburg University of Stuttgart University of Wuppertal University of Leeds University of Leicester | 
| Local coordinator: | W. Soergel, soergel@mathematik.uni-freiburg.de | 
| Research domains: | D-modules Algebraic groups Representation theory of semisimple Lie algebras Representations of Chevalley groups Representations of Kac-Moody algebras and of Quantum groups | 
| Local coordinator: | R. Rentschler, rent@moka.ccr.jussieu.fr | 
| Research domains: | Enveloping algebras Quantum groups Differential operator rings Coadjoint orbits Schubert varieties Quivers | 
| Satellites: | University of Cergy-Pontoise University of Grenoble University of Lyon University of Orsay University of Paris VII University of Poitiers Queen Mary and Westfield College London University of Sheffield University of Reims | 
| Local coordinator: | Ch. Kassel, kassel@math.u-strasbg.fr | 
| Research domains: | Quantum groups and their representation
theory with its applications to Knot  theory Topology and Algebraic geometry Linear algebraic groups Modular representation theory | 
| Local coordinator: | J. Bernstein, bernstei@math.tau.ac.il | 
| Research domains: | Representation theory of Lie groups and their Lie algebras Quantum groups Affine Lie Algebras p-adic groups Automorphic forms | 
| Satellites: | University of Bar-Ilan Hebrew University | 
| Local coordinator: | A. Joseph, joseph@wisdom.weizmann.ac.il | 
| Research domains: | Enveloping algebras Quantum groups Differential operator rings Coadjoint orbits Schubert varieties Deformation theory | 
| Satellites: | University of Haifa School of Technological Education, Holon |