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Hecke Algebras with Unequal Parameters
About this Title
G. Lusztig, Massachusetts Institute of Technology, Cambridge, MA
Publication: CRM Monograph Series
Publication Year:
2003; Volume 18
ISBNs: 978-0-8218-3356-8 (print); 978-1-4704-3863-0 (online)
DOI: https://doi.org/10.1090/crmm/018
MathSciNet review: MR1974442
MSC: Primary 20C08; Secondary 20F55
Table of Contents
Front/Back Matter
Chapters
- Introduction
- Coxeter groups
- Partial order on $W$
- The algebra ${\mathcal H}$
- The bar operator
- The elements $c_w$
- Left or right multiplication by $c_s$
- Dihedral groups
- Cells
- Cosets of parabolic subgroups
- Inversion
- The longest element for a finite $W$
- Examples of elements $D_w$
- The function $\mathbf {a}$
- Conjectures
- Example: The split case
- Example: The quasisplit case
- Example: The infinite dihedral case
- The ring $J$
- Algebras with trace form
- The function ${\mathbf {a}}_E$
- Study of a left cell
- Constructible representations
- Two-sided cells
- Virtual cells
- Relative Coxeter groups
- Representations
- A new realization of Hecke algebras