Seminar on Quantum groups (WISM544)
Fall 2012. 7.5 ects.
This seminar meets every Monday 11:00–12:45 in room 610.

The talks will be typically given by the participants (and sometimes by me).
We will be following Kassel's book on quantum groups. Here are some notes from a recent summer school on quantum groups

Monday Sept 10th: (André)
Introduction to the subject Notes typed by Ralph
Monday Sept 17th: (Ralph & Ludo)
Preliminaries and Tensor products. [Kassel Chapt I and II] Notes by Ralph
Monday Sept 24th: (Reinier)
Hopf algebras. [Kassel Chapt III]
Monday Oct 1st: (Joost N.) Notes by Joost
The quantum plane; q-binomial coefficients [Kassel Chapt IV]
Monday Oct 8th: (Joey)
U_q(g) [Kassel Chapt V and VI; Chari-Pressley p. 208 and 280]
Monday Oct 15th: (Laura)
Duality between SL_q(2) and U_q(sl2). Tensor product of U_q(sl2)-modules.
Monday Oct 22th: (Stephan)
R-matrices and braided tensor categories. [Kassel VIII.1,2,3, XIII.1]
Monday Oct 29th: (Robert) Notes by Robert
Quantum double: construction of R-matrices.
Monday Nov 5th: (Joost B.)
Knots and tangles. The Jones polynomial.
Monday Nov 12th: (Ludo)
Construction fo quantum groups from R-matrices: the FRT construction [Kassel VIII 6-7]
Monday Nov 19th: (Robert) Notes by Robert
Drinfel'd Jimbo algebra U_h(g) [Kassel XVII]
Monday Nov 26th: (Ralph)
Uniqueness of U_h(g) [Kassel XVIII 1-4]
Monday Dec 3rd: (Joost B. en Joost N.)
Quantum dimension, Weyl dimension formula and quantum Weyl dimension formula [Kassel XIV][Fuschs]
Monday Dec 10th: (André)
Integral forms of U_q(g). Vanishing of certian quantum dimensions when q is a root of unitiy. Relashiship to CFT.