2013/02/12 by Cédric Bonnafé, Bonnafé, Cédric
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1302.2721
openalex publication_date 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To each finite Coxeter system (W,S) and to each weight function L, Lusztig has defined the notions of constructible characters and of Lusztig families of W, using the so-called J-induction. Whenever L is constant, and using a general argument, Lusztig has shown that all Lusztig family contains a unique character with minimal b-invariant, and that every constructible character contains an irreducible constituent with minimal b-invariant. We show in this paper that this can be generalized to the case where L is not constant: our proof is by a case-by-case analysis.