One of the beautiful results in the representation theory of the finite groupsis McKays theorem on a correspondence between representations of the binarypolyhed... » 

One of the beautiful results in the representation theory of the finite groupsis McKays theorem on a correspondence between representations of the binarypolyhedral group of SU2 and vertices of an extended simplylaced Dynkindiagram. The Coxeter transformation is the main tool in the proof of the McKaycorrespondence and is closely interrelated with the Cartan matrix andPoincar?? series. The Coxeter functors constructed by Bernstein Gelfand andPonomarev plays a distinguished role in the representation theory of quivers.On these pages the ideas and formulas due to J. N. Bernstein I. M. Gelfandand V. A. Ponomarev H.S.M. Coxeter V. Dlab and C.M. Ringel V. Kac J. McKayT.A. Springer B. Kostant P. Slodowy R. Steinberg W. Ebeling and severalother authors as well as the author and his colleagues from Subbotinsseminar are presented in detail. Several proofs seem to be new. «