MATH 8246 - Representation Theory

Lecturer: Professor Pavlo Pylyavskyy, Vincent Hall 258.

TA: TBA

Time and Location: MWF 10:10 am - 11:00 am, Vincent Hall 206

Website: The class will use UMN Canvas. 

Office Hours: MWF 1:30-2:30pm.

Text: Introduction to Representation Theory, by Etingof et.al. 

Topics: The class will cover

• Representations of algebras: tensor products; indecomposable representations and semisimple algebras; Jordan-Holder and Krull-Schmidt theorems.

• Representations and characters of groups: finite groups and Maschke theorem; characters of finite groups and their orthogonality, character tables; virtual and induced characters; Frobenius formula and Frobenius reciprocity.

• The special case of symmetric groups: Specht modules; Schur-Weyl duality and representations of GL(V).

• Quiver representations: path algebras; indecomposable representations of Dynkin quivers; Gabriel's theorem; reflection functors; projective and injective modules; projective covers.

Grading and Exams: Your grade will be determined by the following:

• • Homework 100%

You are expected to attend lectures.

Homework: It is allowed to collaborate on the homework, however the writing should be done independently.

Official University Statement on Academic Dishonesty: Academic dishonesty in any portion of the academic work for a course shall be grounds for awarding grade of F or N for the entire course.

My Statement on Incompletes, S/N: The grade ``I" is assigned only when a student has satisfactorily (a C- grade or better) completed all but a small portion of the work for the course, and has made prior arrangements to complete the work. This means, for example, if you quit attending class after the first exam, and then request an ``I" in the tenth week, your request will be denied. You will fail the course. To obtain an S, you need at least a C- grade.

Scholastic Conduct: Each student should read his/her college bulletin for the definitions and possible penalties for cheating. During the exams you must do your own work. Students suspected of cheating will be reported to the Scholastic Conduct Committee for appropriate action.

Complaints: You can address complaints about your lecturer to the Associate Director of Undergraduate Studies, Professor Bryan Mosher, Vincent Hall 115.