RSOS Models and Jantzen-Seitz Representations of Hecke Algebras at Roots of Unity

Abstract

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras Hm. We provide an explanation of this coincidence by showing how the irreducible Hm-modules which remain irreducible under restriction to Hm-1 (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of s-fraktur sign and l-fraktur signn.