## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Constructible characters and ${\boldsymbol{b}}$-invariant

C. Bonnafé

#### Abstract

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}.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 3 (2015), 377-390.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1442364585

Digital Object Identifier
doi:10.36045/bbms/1442364585

Mathematical Reviews number (MathSciNet)
MR3396989

Zentralblatt MATH identifier
1328.20008

#### Citation

Bonnafé, C. Constructible characters and ${\boldsymbol{b}}$-invariant. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 377--390. doi:10.36045/bbms/1442364585. https://projecteuclid.org/euclid.bbms/1442364585