# Representation Theory of General Linear Lie Algebra

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. R. Venkatesh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108520)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108520)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01 Basic theory of Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108520/a385f9e85820) (Video)
2. [Lec 02 Basic theory of Lie algebras (Continued).](https://invisiblenetwork.ai/learn/nptel/111108520/0c8e12400477) (Video)
3. [Lec 03 Basic theory of Lie algebras (Continued).](https://invisiblenetwork.ai/learn/nptel/111108520/1c72a678b381) (Video)
4. [Lec 04 Representation theory of Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108520/20ebc37f697e) (Video)
5. [Lec 05 Representation theory of Lie algebras (Continued).](https://invisiblenetwork.ai/learn/nptel/111108520/d369ce04be97) (Video)
6. [Lec 06 Representation of Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108520/580bff880f08) (Video)
7. [Lec 07 Classification of 2 dimensional representation of two dimensional non-abelian Lie algebra.](https://invisiblenetwork.ai/learn/nptel/111108520/6727b658c7b2) (Video)
8. [Lec 08 Isomorphism Theorem.](https://invisiblenetwork.ai/learn/nptel/111108520/08bb86c6630c) (Video)
9. [Lec 09 Characterization of completely reducible module.](https://invisiblenetwork.ai/learn/nptel/111108520/ca91a8deb66f) (Video)
10. [Lec 10 Representation theory of sl2(C).](https://invisiblenetwork.ai/learn/nptel/111108520/9efcc3c76096) (Video)
11. [Lec 11 Irreducible representation of sl2(C)](https://invisiblenetwork.ai/learn/nptel/111108520/793043b0dfd3) (Video)
12. [Lec 12 Irreducible representation of sl2(C) (Continued).](https://invisiblenetwork.ai/learn/nptel/111108520/b7de6b0932af) (Video)
13. [Lec 13 Complete reducibility of sl2(C).](https://invisiblenetwork.ai/learn/nptel/111108520/adf77b38984d) (Video)
14. [Lec 14 Complete reducibility of sl2(C) (continued).](https://invisiblenetwork.ai/learn/nptel/111108520/794d4e302548) (Video)
15. [Lec 15 Representation theory of sl2(C)-basic observation](https://invisiblenetwork.ai/learn/nptel/111108520/8829e7d356fb) (Video)
16. [Lec 16 Application of sl2(C) representation theory in combinatorics.](https://invisiblenetwork.ai/learn/nptel/111108520/5113501f1b1c) (Video)
17. [Lec 17 Constructions of new representations.](https://invisiblenetwork.ai/learn/nptel/111108520/e83242b8bc2e) (Video)
18. [Lec 18 Construction of universal algebras I.](https://invisiblenetwork.ai/learn/nptel/111108520/1635b720e628) (Video)
19. [Lec 19 Construction of universal algebras II](https://invisiblenetwork.ai/learn/nptel/111108520/9be746ddef8c) (Video)
20. [Lec 20 Non-degenerate and invariant bilinear forms.](https://invisiblenetwork.ai/learn/nptel/111108520/d94dbb7db0fd) (Video)
21. [Lec 21 Schur’s lemma and Killing form](https://invisiblenetwork.ai/learn/nptel/111108520/d26bb22f3873) (Video)
22. [Lec 22 Killing form of general and special linear Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108520/bc7b6c8ba66d) (Video)
23. [Lec 23 The universal enveloping algebra.](https://invisiblenetwork.ai/learn/nptel/111108520/9971842b3e22) (Video)
24. [Lec 24 Properties of the universal enveloping algebra](https://invisiblenetwork.ai/learn/nptel/111108520/18e8530d71af) (Video)
25. [Lec 25 The Casimir operator for representations of gln(C) and sln(C).](https://invisiblenetwork.ai/learn/nptel/111108520/42e493c76f13) (Video)
26. [Lec 26 Weyl’s theorem of complete reducibility](https://invisiblenetwork.ai/learn/nptel/111108520/416e0985c6c6) (Video)
27. [Lec 27 The structure of sln+1(C).](https://invisiblenetwork.ai/learn/nptel/111108520/21f55e49be3d) (Video)
28. [Lec 28 Representations of sln+1(C) I.](https://invisiblenetwork.ai/learn/nptel/111108520/df07c4b6c6b7) (Video)
29. [Lec 29 Representations of sln+1(C) II.](https://invisiblenetwork.ai/learn/nptel/111108520/654874177a22) (Video)
30. [Lec 30 Representations of sln+1(C) III.](https://invisiblenetwork.ai/learn/nptel/111108520/bebe7b590dc5) (Video)
31. [Lec 31 Casimir operator and highest weight modules I.](https://invisiblenetwork.ai/learn/nptel/111108520/d62c83868129) (Video)
32. [Lec 32 Casimir operator and highest weight modules II.](https://invisiblenetwork.ai/learn/nptel/111108520/b0447700e2b5) (Video)
33. [Lec 33 Irreducible representations of sln+1(C).](https://invisiblenetwork.ai/learn/nptel/111108520/f134543a087d) (Video)
34. [Lec 34 Verma module and its irreducible quotient.](https://invisiblenetwork.ai/learn/nptel/111108520/1e5910be3d91) (Video)
35. [Lec 35 Verma modules and standard cyclic irreducible modules.](https://invisiblenetwork.ai/learn/nptel/111108520/8d4954502d99) (Video)
36. [Lec 36 Finite dimensional standard cyclic irreducible modules.](https://invisiblenetwork.ai/learn/nptel/111108520/1dcd65c4facc) (Video)
37. [Lec 37 Standard cyclic irreducible modules.](https://invisiblenetwork.ai/learn/nptel/111108520/acc7aa6f8870) (Video)
38. [Lec 38 Character theory.](https://invisiblenetwork.ai/learn/nptel/111108520/0ef44bbbd134) (Video)
39. [Lec 39 Character theory - II](https://invisiblenetwork.ai/learn/nptel/111108520/759f7fb05893) (Video)
40. [Lec 40 Deniminator Identity - Prep 1](https://invisiblenetwork.ai/learn/nptel/111108520/a474530b3455) (Video)
41. [Lec 41 Deniminator Identity - Prep 2](https://invisiblenetwork.ai/learn/nptel/111108520/009365c29fc7) (Video)
42. [Lec 42 Proof of the denominator identity](https://invisiblenetwork.ai/learn/nptel/111108520/77bc1daa1275) (Video)
43. [Lec 43 Freudenthal's formula](https://invisiblenetwork.ai/learn/nptel/111108520/d01f40af2690) (Video)
44. [Lec 44 The Weyl character formula](https://invisiblenetwork.ai/learn/nptel/111108520/5b165e9c639c) (Video)
45. [Lec 45 The Laplacian operator and the Weyl Character Formula](https://invisiblenetwork.ai/learn/nptel/111108520/ff81b2791e70) (Video)
46. [Lec 46 Proof of the Weyl Character Formula](https://invisiblenetwork.ai/learn/nptel/111108520/1ecdc777934d) (Video)
47. [Lec 47 Applications of Weyl Character formula](https://invisiblenetwork.ai/learn/nptel/111108520/500b64f9b022) (Video)
48. [Lec 48 The Weyl dimension formula, Schur polynomials](https://invisiblenetwork.ai/learn/nptel/111108520/1475e2540ace) (Video)
49. [Lec 49 Semi-standard Young Tableaux](https://invisiblenetwork.ai/learn/nptel/111108520/d017f24f7051) (Video)
50. [Lec 50 BGG resolution](https://invisiblenetwork.ai/learn/nptel/111108520/40d8f67252f7) (Video)
51. [Live Session 04-10-2024](https://invisiblenetwork.ai/learn/nptel/111108520/a385f9e85820-2) (Video)