RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity

Omar Foda; Bernard Leclerc; Masato Okado; Jean-Yves Thibon; Trevor A. Welsh

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arXiv · q-alg/9701020

RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity

Omar Foda·Bernard Leclerc·Masato Okado·Jean-Yves Thibon·Trevor A. Welsh

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Abstract

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of 1-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras $H_m$. We provide an explanation of this coincidence by showing how the irreducible $H_m$-modules which remain irreducible under restriction to $H_{m-1}$ (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of affine $\sl_n$.

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Omar Foda, Bernard Leclerc, Masato Okado, Jean-Yves Thibon, Trevor A. Welsh. 1997-01-18. RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity. https://arxiv.org/abs/q-alg/9701020

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