The Quantum Symmetries Seminar is a seminar organized and run by graduate students, for graduate students. The goal of the seminar is to provide graduate students with a space in which to share and discuss topics within the framework of the algebraic presentation of quantum symmetries. The emphasis of the seminar is in clarity and good understanding of the material.

The structure of the seminar consists of weekly meetings on

• Tuesdays in Zoom Meeting 968 3235 1649, at 10:00 am,

please contact the organizers for the password.

This semester we will be reading Jens Carsten Jantzen's Lectures on Quantum Groups, which we will be complementing with Andrew Schopieray's Lie Theory for Fusion Categories: a Research Primer. We have the task of understanding the representation theory of quantized enveloping algebras of simple Lie algebras, with emphasis on the quantized enveloping algebra of the special linear group of dimension two.

Aug 17	Pablo S. Ocal, Organizational meeting.
Aug 25	Pablo S. Ocal, Representations of 𝔰𝔩2.
Aug 31	Pablo S. Ocal, The quantized enveloping algebra Uq(𝔰𝔩2).
Sep 8	Harshit Yadav, Part 1: Representations of Uq(𝔰𝔩2).
Sep 15	Harshit Yadav, Part 2: Representations of Uq(𝔰𝔩2).
Sep 29	Pablo S. Ocal, Part 3: Representations of Uq(𝔰𝔩2).
Oct 6	Pablo S. Ocal, Part 4: Representations of Uq(𝔰𝔩2).
Oct 13	Pablo S. Ocal, Part 5: Representations of Uq(𝔰𝔩2).
Oct 20	Anh Tuong Nguyen, Part 1: Tensor products or: Uq(𝔰𝔩2) as a Hopf algebra.
Nov 3	Anh Tuong Nguyen, Part 2: Tensor products or: Uq(𝔰𝔩2) as a Hopf algebra.
Nov 10	Anh Tuong Nguyen, Part 3: Tensor products or: Uq(𝔰𝔩2) as a Hopf algebra.
Nov 24	Harshit Yadav, Lie algebras.
Dec 1	Anh Tuong Nguyen, Representation theory of semisimple Lie algebras.
Dec 15	Pablo S. Ocal, Representation theory of quantized enveloping algebras.

Errata to Jantzen's lectures can be found in:

• Errata to Lectures on Quantum Groups (1st Edition) by Jens Carsten Jantzen.
• Errata to Lectures on Quantum Groups (2nd Edition) by Jens Carsten Jantzen.

The representations of the special linear Lie algebra of order two can be found in:

• Lie Algebras by Aleksander Horawa.

Some useful facts about universal enveloping algebras (as well as about the basics of finite dimensional representations of semisimple Lie algebras) can be found in:

• Representation theory of semisimple Lie Algebras by Dan Ciubotaru.

The representations of the universal enveloping algebra of the special linear Lie algebra of order two can be found in:

• Characteristic zero: A Tour of Representation Theory by Martin Lorenz.
• Positive characteristic: Lie Algebras by Ivan Losev.

A book that may be helpful to deepen into the material covered is:

• Representations of Algebraic Groups by Jens Carsten Jantzen.

The goals achieved were the coverage of Chapters 0, 1, 2, and 3 of Jantzen's "Lectures on Quantum Groups" and Sections 1, 2, and 3 of Schopieray's "Lie Theory for Fusion Categories: a Research Primer", in extensive detail (including additional examples and exercises). These readings were continued during the Spring 2021 Quantum Symmetries Seminar.

The past edition of the Quantum Symmetries Seminar is:

• Fall 2019.