Combinatorics of the "coincidental" reflection groups

author: Vic Reiner, University of Minnesota
presenter: Nathan Williams, University of Minnesota
published: July 19, 2019,   recorded: July 2019,   views: 115


Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


Much modern combinatorics involves finite reflection groups, both real and complex. Mysteriously, many results work particularly well for the so-called "coincidental" reflection groups. These are the groups generated by n reflections acting in n-dimensional space whose exponents form an arithmetic sequence – they are the real reflection groups of types A, B/C, H3, dihedral groups, and all non-real Shephard groups (the symmetries of regular complex polytopes). This talk will discuss recent work featuring the coincidental groups. This includes recent work with Shepler and Sommers uncovering their extra elegant invariant theory, leading to product formulas for the face numbers and h-vectors of their associated cluster complexes, and a q-analogue of the transformation taking the h-vector to f-vector. We also hope to discuss theorems and conjectures of various others, such as Alex Miller, Barnard–Reading, Hamaker–Patrias–Pechenik–Williams, and Sam Hopkins.

See Also:

Download slides icon Download slides: FPSAC2019_williams_reflection_groups_01.pdf (22.3 MB)

Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: