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Group Representations 1 - NMAG438

Title:	Reprezentace grup 1
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://www.karlin.mff.cuni.cz/~stanovsk/vyuka/repre.htm

Guarantor:	doc. Mgr. Pavel Růžička, Ph.D. RNDr. Zuzana Patáková, Ph.D.
Class:	M Mgr. MSTR M Mgr. MSTR > Povinně volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NALG021
Interchangeability :	NALG021
Is interchangeable with:	NALG021

Opinion survey results Examination dates Noticeboard

Annotation -

Elements of theory of representations of groups. The course may not be taught every academic year, it will be taught at least once every two years.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2019)

Course completion requirements -

See the website of the course.

Last update: Stanovský David, doc. RNDr., Ph.D. (16.02.2024)

Literature -

Primary:

lecture notes by Travis Schedler:

https://www.imperial.ac.uk/people/t.schedler/document/8765/lecture-notes/?lecture-notes.pdf

lecture notes by Benjamin Steinberg:

https://users.metu.edu.tr/sozkap/513-2013/Steinberg.pdf

Secondary:

1. Charles W. Curtis, Irving Reiner: Representation theory of finite groups and associative algebras, John Wiley & Sons, New York, 1988.

2. Walter Feit: The representation theory of finite groups, North-Holland mathematical library, Amsterdam, 1982

3. Steven H. Weintraub: Representation Theory of Finite Groups: Algebra and Arithmetic (Graduate Studies in Mathematics, Vol. 59), AMS, Providence 2003.

Last update: Stanovský David, doc. RNDr., Ph.D. (17.02.2024)

Requirements to the exam -

See the website of the course.

Last update: Stanovský David, doc. RNDr., Ph.D. (17.02.2024)

Syllabus -

1. Fundamentals of representation theory: Maschke's theorem, Schur's lemma, counting representations, direct and tensor product of representations, module-theoretic approach

2. Characters, orthogonality relation.

3. Representations of the symmetric group, hook length formula

4. The degree theorem, Burnside's pq theorem

5. Fourier analysis on finite groups

Last update: Stanovský David, doc. RNDr., Ph.D. (17.02.2024)

Entry requirements -

Linear algebra and basics of the group theory and commutative algebra on the level of the introductory course in abstract algebra.

Last update: Stanovský David, doc. RNDr., Ph.D. (17.02.2024)