Glasgow Mathematical Journal

Research Article

RECURRENCE RELATIONS, DYNKIN DIAGRAMS AND PLÜCKER FORMULAE

JOHN M. BURNSa1 and MICHAEL J. CLANCYa2

a1 Department of Mathematics, National University of Ireland, Galway, Ireland

a2 School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

Abstract.

We prove a generalisation of an observation of N. Iwahori concerning the coefficients of the extended Dynkin diagram of a complex simple Lie algebra. We relate the combinatorics of these coefficients to the orders of finite groups that act discontinuously on the Riemann sphere and to the Plücker formulae.

(Received January 27 2006)

(Revised September 27 2006)

Key Words:

  • 17B20