Representation Theory of Finite Groups 2EEWA5PZP4

URI	`m2://res/2EEWA5PZP4`
Kind	course
Creators	R. Venkatesh (instructor)
Date	2025-12-17
MSC	20-XX
Scope	in
Ids	course 04dese585:111108898

Expressions

e1: edition

Language	en
Date	2025-12-17

m1: page, IISc Bangalore (record). nptel 111108898
m2: page, 2025-12-17 (record). nptel 111108898

Contents

part 1: Week 1 Review: Basic Linear Algebra
session 1: Basics of vector spaces
session 2: Inner product spaces
session 3: Diagonalization
session 4: Generalized eigen spaces
session 5: Decomposition theorems
part 2: Week 2 Representation Theory: An introduction through basic linear algebra, Representations of finite cyclic groups
session 6: Definition of representation
session 7: Isomorphism theorems
session 8: Indecomposable representations
session 9: Schur's Lemma
session 10: Filtration of representations
part 3: Week 3 Representations of groups and algebras: definitions, examples, indecomposable (decomposable) representations, reducible (irreducible) representations
session 11: Construction of new representations by extensions
session 12: Basics of representation theory of finite groups
session 13: Classification of irreducible representations of finite cyclic group and Symmteric group
session 14: Irreducibility via Cyclic Vectors
session 15: Construction of representations of group generated by a set with defining relations
part 4: Week 4 Complete reducibility of finite dimensional representations of finite groups and basic properties of character theory
session 16: Complete reducibility of unitary representations
session 17: Complete reducibility of finite dimensional representations of finite groups
session 18: Projection map from representation of G to its fixed subspace
session 19: Character Theory: Basic properties
session 20: Orthogonality relations of irreducible characters of finite group
part 5: Week 5 Schur orthogonality relations, regular representation, and its decomposition
session 21: Orthonormal subset of space of class functions and Orthogonality of irreducible characters
session 22: Schur's orthogonality relations and its applications
session 23: Applications of character theory
session 24: Regular representation, decomposition of regular representation
session 25: Orthonormal basis of space of class functions and computation of character tables
part 6: Week 6 Second Orthogonality relations, Classification of irreducible characters of abelian group, Dimension theorem and its aplications
session 26: Orthogonality of the columns of the character table
session 27: Representations of finite abeilian group
session 28: Algebraic numbers and equivalent conditions for algebraic integers
session 29: Dimension theorem
session 30: Applications of dimension theorem
part 7: Week 7 Character tables of some finite groups, Burnside Theorem, Tensor product space
session 31: Character table computation of groups: Q_8, D_8, A_4
session 32: Burnside Theorem and its proof
session 33: Proof of key result used in Burnside Theorem
session 34: Notion of Tensor product
session 35: Basic properties of Tensor product
part 8: Week 8 Tensor product, Symmetric tensor, alternating tensor product
session 36: Symmetric tensor product
session 37: Alternating tensor product
session 38: G-action on Symmetric and exterior tensor product
session 39: Graded character of Symmetric tensor algebra and exterior algebra
session 40: Alternate proof of orthogonality of irreducible characters
part 9: Week 9 Density theorem, Frobenius theorem, Induced representation, Frobenius reciprocity and Mackey's restriction formula
session 41: Density theorem
session 42: Frobenius theorem
session 43: Induced representation
session 44: Frobenius reciprocity
session 45: Mackey's restrcition formula
part 10: Week 10 Mackey's irreducibility criterion, Fourier analysis on finite groups, Fourier transform, Cayley graph
session 46: Mackey's irreducibility criterion
session 47: Fourier analysis on finite groups
session 48: Fourier inversion
session 49: Fourier analysis on nonabeilian groups
session 50: Applications of Fourier analysis on finite groups
part 11: Week 11 Eigenvalues of Cayley graph, combinatorics in symmetric group and introduction to representation theory of symmetric group
session 51: Cayley graph and its eigenvalues
session 52: Notations and combinatorics in representation theory of symmetric group
session 53: Irreducible representations of symmetric group
part 12: Week 12 Permutation modules, construction and classification of irreducible representations of symmeric group
session 54: Permutation modules
session 55: Constructing irreducibles of symmetric group
session 56: Classification of irreducible representations of symmetric group

Catalogue records

nptel: 111108898 (manifestation)
nptel_video: 111108898 (manifestation)