Fall 2012.

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

Introduction to the subject Notes typed by Ralph

Preliminaries and Tensor products. [Kassel Chapt I and II] Notes by Ralph

Hopf algebras. [Kassel Chapt III]

The quantum plane; q-binomial coefficients [Kassel Chapt IV]

U_q(g) [Kassel Chapt V and VI; Chari-Pressley p. 208 and 280]

Duality between SL_q(2) and U_q(sl2). Tensor product of U_q(sl2)-modules.

R-matrices and braided tensor categories. [Kassel VIII.1,2,3, XIII.1]

Quantum double: construction of R-matrices.

Knots and tangles. The Jones polynomial.

Construction fo quantum groups from R-matrices: the FRT construction [Kassel VIII 6-7]

Drinfel'd Jimbo algebra U

Uniqueness of U

Quantum dimension, Weyl dimension formula and quantum Weyl dimension formula [Kassel XIV][Fuschs]

Integral forms of U