1997/01/18 by Omar Foda, Bernard Leclerc, Foda, Omar +7
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #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/9701021
openalex publication_date 1997/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of n-regular partitions label both of the following classes of objects: 1. The spectrum of unrestricted solid-on-solid lattice models based on level-1 representations of the affine algebras \sln, 2. The irreducible representations of type-A Hecke algebras at roots of unity: Hm(√[n]1). Secondly, we show that a certain subset of the n-regular partitions label both of the following classes of objects: 1. The spectrum of restricted solid-on-solid lattice models based on cosets of affine algebras (sl(n)^1 × sl(n)^1)/ sl(n)^2. 2. Jantzen-Seitz (JS) representations of Hm(√[n]1): irreducible representations that remain irreducible under restriction to Hm-1(√[n]1). Using the above relationships, we characterise the JS representations of Hm(√[n]1) and show that the generating series that count them are branching functions of affine \sln.