Notes written by Arun Ram, 2005

I am hoping that 2005 will be a productive year. The following are incomplete notes that I have worked on this year. I thank the Centre Bernoulli at the EPFL Lausanne and the Max-Planck-Institut fur Mathematik in Bonn for support and hospitality during this work. This research is also partially supported by the National Science Foundation and a Vilas Associates award at the University of Wisconsin--Madison.

Some of this material is based upon work supported by the National Science Foundation under Grant No. 0353038. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

The following is the start of what will hopefully someday be a book on Combinatorial Representation Theory


Quantum groups


Quantum group representations

Almost semisimple algebras

Reflection groups

Hecke algebras

Diagram algebras

(1) Reflection groups, refgpdef1.24.05.pdf .

(2) The reflection group G_4, refgps1.21.05.pdf

(3) Dihedral groups G_{r,r,2}, refgps1.21.05.pdf

(4) The path model, pathmodel1.15.05.pdf

(5) Yangians, ygnsBonn2.08.05.pdf

(6) Convolution algebras, convalgs1.24.05.pdf

(7) Basic constructions, basicconst2.16.05.pdf

(8) Temperley-Lieb algebras, TLalg2.13.05.pdf

(9) Homological algebra, homalg2.16.05.pdf .

(10) Kazhdan-Lusztig polynomials KLpolys2.28.05.pdf .