NOC:Representation Theory of General Linear Lie Algebra

Lecture 1 - Basic Theory of Lie algebras

Lecture 2 - Basic Theory of Lie algebras (Continued...)

Lecture 3 - Basic Theory of Lie algebras (Continued...)

Lecture 4 - Representation Theory of Lie algebras

Lecture 5 - Representation Theory of Lie algebras (Continued...)

Lecture 6 - Representation of Lie algebras

Lecture 7 - Classification of 2 dimensional representation of two dimensional non-abelian Lie algebra

Lecture 8 - Isomorphism Theorem

Lecture 9 - Characterization of completely reducible module

Lecture 10 - Representation theory of sl2(C)

Lecture 11 - Irreducible representation of sl2(C)

Lecture 12 - Irreducible representation of sl2(C) (Continued...)

Lecture 13 - Complete reducibility of sl2(C)

Lecture 14 - Complete reducibility of sl2(C) (Continued...)

Lecture 15 - Representation theory of sl2(C)-basic observation

Lecture 16 - Application of sl2(C) representation theory in combinatorics

Lecture 17 - Constructions of new representations

Lecture 18 - Construction of universal algebras - I

Lecture 19 - Construction of universal algebras - II

Lecture 20 - Non-degenerate and invariant bilinear forms

Lecture 21 - Schur’s lemma and Killing form

Lecture 22 - Killing form of general and special linear Lie algebras

Lecture 23 - The universal enveloping algebra

Lecture 24 - Properties of the universal enveloping algebra

Lecture 25 - The Casimir operator for representations of gln(C) and sln(C)

Lecture 26 - Weyl’s theorem of complete reducibility

Lecture 27 - The structure of sln+1(C)

Lecture 28 - Representations of sln+1(C) - I

Lecture 29 - Representations of sln+1(C) - II

Lecture 30 - Representations of sln+1(C) - III

Lecture 31 - Casimir operator and highest weight modules - I

Lecture 32 - Casimir operator and highest weight modules - II

Lecture 33 - Irreducible representations of sln+1(C)

Lecture 34 - Verma module and its irreducible quotient

Lecture 35 - Verma modules and standard cyclic irreducible modules

Lecture 36 - Finite dimensional standard cyclic irreducible modules

Lecture 37 - Standard cyclic irreducible modules

Lecture 38 - Character Theory - I

Lecture 39 - Character Theory - II

Lecture 40 - Deniminator Identity - Prep 1

Lecture 41 - Deniminator Identity - Prep 2

Lecture 42 - Proof of the denominator identity

Lecture 43 - Freudenthal's formula

Lecture 44 - The Weyl character formula

Lecture 45 - The Laplacian operator and the Weyl Character Formula

Lecture 46 - Proof of the Weyl Character Formula

Lecture 47 - Applications of Weyl Character formula

Lecture 48 - The Weyl dimension formula, Schur polynomials

Lecture 49 - Semi-standard Young Tableaux

Lecture 50 - BGG resolution