Standard Young tableaux for finite root systems

Abstract

The study of representations of affine Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any finite Coxeter group. This paper is completely independent of affine Hecke algebra theory and is purely combinatorial. We define generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root systems of Type A. The classical notions of conjugation of shapes, ribbon shapes, axial distances, and the row reading and column reading standard tableaux, have natural generalizations to the root system case. In the final section we give an interpretation of the shapes and standard tableaux for root systems of Type C which is in a form similar to classical theory of shapes and standard tableaux.