2012/10/24 by Alexander Kleshchev, Kleshchev, Alexander S. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1210.6556
openalex publication_date 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A cuspidal system for an affine Khovanov-Lauda-Rouquier algerba R_\al yields a theory of standard modules. This allows us to classify the irreducible modules over R_\al up to the so-called imaginary modules. We make a conjecture on reductions modulo p of irreducible R_\al-modules, which generalizes James Conjecture. We also describe minuscule imaginary modules, laying the groundwork for future study of imaginary Schur-Weyl duality. We introduce colored imaginary tensor spaces and reduce a classification of imaginary modules to one color. We study the characters of cuspidal modules. We show that under the Khovanov-Lauda-Rouquier categorification, cuspidal modules correspond to dual root vectors.