1999/02/01 by Bernard Leclerc, Leclerc, Bernard · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #MSC 17B 20C #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B #msc:20C
paper · pdf · doi:10.48550/arxiv.math/9902006
10 pages
arxiv created 1999/02/01 · openalex publication_date 1999/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an n-th root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space previously introduced in a joint work with Thibon. It follows that these coefficients can all be expressed in terms of those of the global crystal basis of the irreducible sub-representation generated by the vacuum vector. As a consequence, using works of Ariki and Varagnolo-Vasserot, it is possible to give a new proof of Lusztig's character formula for the simple Uv(slr)-modules at roots of unity, which does not involve representations of sl^r of negative level.