MATH-334 / 5 credits

Teacher:

Language: English

Remark: pas donné en 2023-24

## Summary

Study the basics of representation theory of groups and associative algebras.

## Keywords

Linear representation, subrepresentation, quotient, simple representation, subrepresentation, quotient representation, semisimple representation, character of a representation, associative algebra, representation of a finite group.

## Required courses

Linear algebra or Advanced Linear algebra; Group theory

## Recommended courses

Lie algebras, Coxeter groups

## Learning Outcomes

By the end of the course, the student must be able to:

• Apply concepts and ideas of the course
• Reason rigorously using the notions of the course
• Choose an appropriate method to solve problems
• Identify the concepts relevant to each problem
• Apply concepts to solve problems similar to the questions in problem sets
• Solve new problems using the ideas of the course
• Implement appropriate methods to study and construct representations of groups and algebras

## Teaching methods

Lectures and exercise sessions

## Assessment methods

One take-home written assignment (15% of the grade)

Written exam (85% of the grade)

## Supervision

 Office hours No Assistants Yes Forum No

## Bibliography

1. P. Etingof, O. Goldberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina, "Introduction to Representation Theory".   Student Mathematical Library Volume: 59; 2011. ISBN: 978-0-8218-5351-1

2. Fulton, William, and Joe Harris. Representation Theory: A First Course. Graduate texts in mathematics. Vol. 129. New York, NY: Springer, 1991. ISBN: 9780387974958.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Representation theory
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

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