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Course, academic year 2023/2024
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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 2023
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. RNDr. David Stanovský, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG021
Interchangeability : NALG021
Is interchangeable with: NALG021
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (14.05.2019)
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.
Course completion requirements -
Last update: doc. RNDr. David Stanovský, Ph.D. (16.02.2024)

See the website of the course.

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

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.

Requirements to the exam -
Last update: doc. RNDr. David Stanovský, Ph.D. (17.02.2024)

See the website of the course.

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

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

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

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

 
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