Open Access
august 2015 Constructible characters and ${\boldsymbol{b}}$-invariant
C. Bonnafé
Bull. Belg. Math. Soc. Simon Stevin 22(3): 377-390 (august 2015). DOI: 10.36045/bbms/1442364585


If $W$ is a finite Coxeter group and $\varphi$ is a weight function, Lusztig has defined {\it $\\varphi$-constructible characters} of $W$, as well as a partition of the set of irreducible characters of $W$ into {\it Lusztig $\varphi$-families}. We prove that every Lusztig $\varphi$-family contains a unique character with minimal $b$-invariant, and that every $\varphi$-constructible character has a unique irreducible constituent with minimal $b$-invariant. This generalizes Lusztig's result about {\it special characters} to the case where $\varphi$ is not constant. This is compatible with some conjectures of Rouquier and the author about {\it Calogero-Moser families} and {\it Calogero-Moser cellular characters}.


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C. Bonnafé. "Constructible characters and ${\boldsymbol{b}}$-invariant." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 377 - 390, august 2015.


Published: august 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1328.20008
MathSciNet: MR3396989
Digital Object Identifier: 10.36045/bbms/1442364585

Primary: 20C08 , 20F55

Keywords: $b$-invariant , cellular characters , Coxeter groups , families

Rights: Copyright © 2015 The Belgian Mathematical Society

Vol.22 • No. 3 • august 2015
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