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

1997/01/18 by Omar Foda, Bernard Leclerc, Foda, Omar +7
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9701020

openalex publication_date 1997/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

Related

• Combinatorics of solvable lattice models, and modular representations of Hecke algebras
• Residue symbols and Jantzen-Seitz partitions
• Partition Algebras and the Invariant Theory of the Symmetric Group
• Resolving Irreducible ℂS_n-Modules by Modules Restricted from GL_n(ℂ)
• Kronecker positivity and 2-modular representation theory