Length functions and reduced words for complex reflection groups
- K. Bremke and G. Malle, Reduced words and a length function
for G(e,1,n), Indag. Math. (N.S.) 8, 453–469.
- K. Bremke and G. Malle, Root systems and length functions,
Geom. Dedicata 72 (1998), 83–97.
Hyperbolic Coxeter groups (C. Egedy)
- Sections 6.8–6.9 of Humphreys' book; see also the
references that he gives there.
Quaternionic reflection groups
- A. M. Cohen, Finite quaternionic reflection groups,
J. Algebra 64 (1980), 293–324.
- G. Lusztig, A class of irreducible representations of a Weyl
group, Nederl. Akad. Wetensch. Indag. Math. 41
Braid groups (A. Lowrance)
There are many, many other papers on braid groups that would also make
suitable topics for a talk. This one in particular, however, is
important for us because its main result is the motivation for the
definition of the Hecke algebra of a complex reflection group.
- E. Brieskorn, Die Fundamentalgruppe des Raumes der
regulären Orbits einer endlichen komplexen
Spiegelungsgruppe, Invent. Math 12 (1971)
Knot and link invariants (G. Pruidze)
- Section 4.5 of Geck–Pfeiffer, and other references given
“Coxeter-type” presentations for complex reflection groups
- D.W. Koster's Ph.D. thesis, University of Wisconsin–Madison,
1976. (See me for a copy.)
- M. Broué, G. Malle, R. Rouquier, Complex reflection
groups, braid groups, Hecke algebras, J. Reine
Agnew. Math 500 (1999), 127–190.
“Crystallographic” root systems for complex reflection groups
Recall that crystallographicity is an integrality condition on the
root system. The fascinating idea in this paper is that if we replace
Z by the ring of algebraic integers in a suitable number
field, then all complex
reflection groups, including all finite Coxeter
groups, may be thought of “crystallographic.”
- G. Nebe, The root lattices of the complex reflection
groups, J. Group Theory 2 (1999), 15–38.
Other topics . . .
The last chapter of Humphreys' book is a brief summary of a number of
interesting topics that one can explore starting from a basic
knowledge of Coxeter groups. Any one of these would make a
suitable topic for a talk. You would probably want get a bit
deeper into the subject than what's in Humphreys' book, but he
provides a good list of references for each topic.
The word problem (S. Gaudet)
Reflection groups in Lie theory (M. Laubinger)