# Representation Theory of Finite Groups

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. R. Venkatesh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108898)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108898)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Basics of vector spaces](https://invisiblenetwork.ai/learn/nptel/111108898/632acabbd070) (Video)
2. [Inner product spaces](https://invisiblenetwork.ai/learn/nptel/111108898/a2ebaadefc09) (Video)
3. [Diagonalization](https://invisiblenetwork.ai/learn/nptel/111108898/77e51db01037) (Video)
4. [Generalized eigen spaces](https://invisiblenetwork.ai/learn/nptel/111108898/7280f13e2d9c) (Video)
5. [Decomposition theorems](https://invisiblenetwork.ai/learn/nptel/111108898/3b53eb27eae9) (Video)
6. [Definition of representation](https://invisiblenetwork.ai/learn/nptel/111108898/cb16834f8a50) (Video)
7. [Isomorphism theorems](https://invisiblenetwork.ai/learn/nptel/111108898/d5271b907d16) (Video)
8. [Indecomposable representations](https://invisiblenetwork.ai/learn/nptel/111108898/264279a0b0ae) (Video)
9. [Schur's Lemma](https://invisiblenetwork.ai/learn/nptel/111108898/1f91e13c568f) (Video)
10. [Filtration of representations](https://invisiblenetwork.ai/learn/nptel/111108898/13f2c4f9205e) (Video)
11. [Construction of new representations by extensions](https://invisiblenetwork.ai/learn/nptel/111108898/c19b1d547246) (Video)
12. [Basics of representation theory of finite groups](https://invisiblenetwork.ai/learn/nptel/111108898/746df6ba5e64) (Video)
13. [Classification of irreducible representations of finite cyclic group and Symmteric group](https://invisiblenetwork.ai/learn/nptel/111108898/0286ff839ea8) (Video)
14. [Irreducibility via Cyclic Vectors](https://invisiblenetwork.ai/learn/nptel/111108898/915bf73b518a) (Video)
15. [Construction of representations of group generated by a set with defining relations](https://invisiblenetwork.ai/learn/nptel/111108898/5fb7846d0bf2) (Video)
16. [Complete reducibility of unitary representations](https://invisiblenetwork.ai/learn/nptel/111108898/58cddd4e3623) (Video)
17. [Complete reducibility of finite dimensional representations of finite groups](https://invisiblenetwork.ai/learn/nptel/111108898/90d491cc9add) (Video)
18. [Projection map from representation of G to its fixed subspace](https://invisiblenetwork.ai/learn/nptel/111108898/3c500978d035) (Video)
19. [Character Theory: Basic properties](https://invisiblenetwork.ai/learn/nptel/111108898/4e6b35cb2e74) (Video)
20. [Orthogonality relations of irreducible characters of finite group](https://invisiblenetwork.ai/learn/nptel/111108898/80c85f3fabb1) (Video)
21. [Orthonormal subset of space of class functions and Orthogonality of irreducible characters](https://invisiblenetwork.ai/learn/nptel/111108898/96af7a3e4697) (Video)
22. [Schur's orthogonality relations and its applications](https://invisiblenetwork.ai/learn/nptel/111108898/d3a468258128) (Video)
23. [Applications of character theory](https://invisiblenetwork.ai/learn/nptel/111108898/ab479a9a0125) (Video)
24. [Regular representation, decomposition of regular representation](https://invisiblenetwork.ai/learn/nptel/111108898/25644d91a8cf) (Video)
25. [Orthonormal basis of space of class functions and computation of character tables](https://invisiblenetwork.ai/learn/nptel/111108898/c6eefaaf177d) (Video)
26. [Orthogonality of the columns of the character table](https://invisiblenetwork.ai/learn/nptel/111108898/d4fbe7052cd0) (Video)
27. [Representations of finite abeilian group](https://invisiblenetwork.ai/learn/nptel/111108898/dc9fb6a48365) (Video)
28. [Algebraic numbers and equivalent conditions for algebraic integers](https://invisiblenetwork.ai/learn/nptel/111108898/274ee3269adc) (Video)
29. [Dimension theorem](https://invisiblenetwork.ai/learn/nptel/111108898/1c34c5c15e11) (Video)
30. [Applications of dimension theorem](https://invisiblenetwork.ai/learn/nptel/111108898/686e028a84b9) (Video)
31. [Character table computation of groups: Q_8, D_8, A_4](https://invisiblenetwork.ai/learn/nptel/111108898/e634862d2c94) (Video)
32. [Burnside Theorem and its proof](https://invisiblenetwork.ai/learn/nptel/111108898/25a4468ebaf7) (Video)
33. [Proof of key result used in Burnside Theorem](https://invisiblenetwork.ai/learn/nptel/111108898/31a0b69c6f94) (Video)
34. [Notion of Tensor product](https://invisiblenetwork.ai/learn/nptel/111108898/fa88c2f86afe) (Video)
35. [Basic properties of Tensor product](https://invisiblenetwork.ai/learn/nptel/111108898/6f64dd240132) (Video)
36. [Symmetric tensor product](https://invisiblenetwork.ai/learn/nptel/111108898/40cd655a07d6) (Video)
37. [Alternating tensor product](https://invisiblenetwork.ai/learn/nptel/111108898/7256458d117c) (Video)
38. [G-action on Symmetric and exterior tensor product](https://invisiblenetwork.ai/learn/nptel/111108898/813522fc5cf7) (Video)
39. [Graded character of Symmetric tensor algebra and exterior algebra](https://invisiblenetwork.ai/learn/nptel/111108898/12d199316d82) (Video)
40. [Alternate proof of orthogonality of irreducible characters](https://invisiblenetwork.ai/learn/nptel/111108898/44d1ddf86886) (Video)
41. [Density theorem](https://invisiblenetwork.ai/learn/nptel/111108898/0df5aefc778f) (Video)
42. [Frobenius theorem](https://invisiblenetwork.ai/learn/nptel/111108898/5b3895931c4d) (Video)
43. [Induced representation](https://invisiblenetwork.ai/learn/nptel/111108898/add7768abb24) (Video)
44. [Frobenius reciprocity](https://invisiblenetwork.ai/learn/nptel/111108898/bb00593cf470) (Video)
45. [Mackey's restrcition formula](https://invisiblenetwork.ai/learn/nptel/111108898/c3ed71f27374) (Video)
46. [Mackey's irreducibility criterion](https://invisiblenetwork.ai/learn/nptel/111108898/6af71b17f3fd) (Video)
47. [Fourier analysis on finite groups](https://invisiblenetwork.ai/learn/nptel/111108898/e8affc578722) (Video)
48. [Fourier inversion](https://invisiblenetwork.ai/learn/nptel/111108898/ba49bfb0caa1) (Video)
49. [Fourier analysis on nonabeilian groups](https://invisiblenetwork.ai/learn/nptel/111108898/0f2b7724cea4) (Video)
50. [Applications of Fourier analysis on finite groups](https://invisiblenetwork.ai/learn/nptel/111108898/76c64dd5885e) (Video)
51. [Cayley graph and its eigenvalues](https://invisiblenetwork.ai/learn/nptel/111108898/9b3483252b1a) (Video)
52. [Notations and combinatorics in representation theory of symmetric group](https://invisiblenetwork.ai/learn/nptel/111108898/25f6d2ba90bf) (Video)
53. [Irreducible representations of symmetric group](https://invisiblenetwork.ai/learn/nptel/111108898/0312bfdf3aae) (Video)
54. [Permutation modules](https://invisiblenetwork.ai/learn/nptel/111108898/50c8e9d42644) (Video)
55. [Constructing irreducibles of symmetric group](https://invisiblenetwork.ai/learn/nptel/111108898/de96c6f21fb4) (Video)
56. [Classification of irreducible representations of symmetric group](https://invisiblenetwork.ai/learn/nptel/111108898/9bfcc38a712e) (Video)