Math 2.0

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Representation Theory of General Linear Lie Algebra KCPCPEVAWZ

URIm2://res/KCPCPEVAWZ
Kindcourse
CreatorsR. Venkatesh (instructor)
Date2024-07-04
Scopein
Idscourse 04dese585:111108520

Expressions

e1: edition

Languageen
Date2024-07-04
Contents
  • part 1: week-01
  • session 1: Lec 01 Basic theory of Lie algebras.
  • session 2: Lec 02 Basic theory of Lie algebras (Continued).
  • session 3: Lec 03 Basic theory of Lie algebras (Continued).
  • session 4: Lec 04 Representation theory of Lie algebras.
  • session 5: Lec 05 Representation theory of Lie algebras (Continued).
  • part 2: week-02
  • session 6: Lec 06 Representation of Lie algebras.
  • session 7: Lec 07 Classification of 2 dimensional representation of two dimensional non-abelian Lie algebra.
  • session 8: Lec 08 Isomorphism Theorem.
  • session 9: Lec 09 Characterization of completely reducible module.
  • session 10: Lec 10 Representation theory of sl2(C).
  • part 3: week-03
  • session 11: Lec 11 Irreducible representation of sl2(C)
  • session 12: Lec 12 Irreducible representation of sl2(C) (Continued).
  • session 13: Lec 13 Complete reducibility of sl2(C).
  • session 14: Lec 14 Complete reducibility of sl2(C) (continued).
  • session 15: Lec 15 Representation theory of sl2(C)-basic observation
  • session 16: Lec 16 Application of sl2(C) representation theory in combinatorics.
  • part 4: week-04
  • session 17: Lec 17 Constructions of new representations.
  • session 18: Lec 18 Construction of universal algebras I.
  • session 19: Lec 19 Construction of universal algebras II
  • session 20: Lec 20 Non-degenerate and invariant bilinear forms.
  • session 21: Lec 21 Schur’s lemma and Killing form
  • part 5: week-05
  • session 22: Lec 22 Killing form of general and special linear Lie algebras.
  • session 23: Lec 23 The universal enveloping algebra.
  • session 24: Lec 24 Properties of the universal enveloping algebra
  • session 25: Lec 25 The Casimir operator for representations of gln(C) and sln(C).
  • part 6: week-06
  • session 26: Lec 26 Weyl’s theorem of complete reducibility
  • session 27: Lec 27 The structure of sln+1(C).
  • session 28: Lec 28 Representations of sln+1(C) I.
  • session 29: Lec 29 Representations of sln+1(C) II.
  • part 7: week-07
  • session 30: Lec 30 Representations of sln+1(C) III.
  • session 31: Lec 31 Casimir operator and highest weight modules I.
  • session 32: Lec 32 Casimir operator and highest weight modules II.
  • session 33: Lec 33 Irreducible representations of sln+1(C).
  • session 34: Lec 34 Verma module and its irreducible quotient.
  • part 8: week-08
  • session 35: Lec 35 Verma modules and standard cyclic irreducible modules.
  • session 36: Lec 36 Finite dimensional standard cyclic irreducible modules.
  • session 37: Lec 37 Standard cyclic irreducible modules.
  • session 38: Lec 38 Character theory.
  • part 9: week-09
  • session 39: Lec 39 Character theory - II
  • session 40: Lec 40 Deniminator Identity - Prep 1
  • session 41: Lec 41 Deniminator Identity - Prep 2
  • session 42: Lec 42 Proof of the denominator identity
  • part 10: week-10
  • session 43: Lec 43 Freudenthal's formula
  • session 44: Lec 44 The Weyl character formula
  • session 45: Lec 45 The Laplacian operator and the Weyl Character Formula
  • session 46: Lec 46 Proof of the Weyl Character Formula
  • part 11: week-11
  • session 47: Lec 47 Applications of Weyl Character formula
  • session 48: Lec 48 The Weyl dimension formula, Schur polynomials
  • part 12: week-12
  • session 49: Lec 49 Semi-standard Young Tableaux
  • session 50: Lec 50 BGG resolution
  • part 13: Live Session
  • session 51: Live Session 04-10-2024

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