MAT 543 Syllabus Representation Theory Fall 2025

The schedule for topics covered in lecture is as follows. Please do the assigned reading prior to lecture. This will make the lectures more effective for you.

• Monday, August 25
  Representations of finite groups
  
  
• Wednesday, August 27
  Characters
  
  
• Monday, September 1
  NO LECTURE
  
  
• Wednesday, September 3
  Examples, induced representations, group algebras and real representations
  Problem Set 1 due in lecture.
  
  
• Monday, September 8
  Representations of symmetric groups, Young diagrams and the Frobenius character formula
  
  
• Wednesday, September 10
  Representations of alternating groups and general linear groups over finite fields
  Problem Set 2 due in lecture.
  
  
• Monday, September 15
  Weyl's construction
  
  
• Wednesday, September 17
  Lie groups
  Problem Set 3 due in lecture.
  
  
• Monday, September 22
  Lie algebras
  
  
• Wednesday, September 24
  Initial classification of Lie algebras
  Problem Set 4 due in lecture.
  
  
• Monday, September 29
  Lie algebras in dimensions one, two and three
  
  
• Wednesday, October 1
  Representations of the special linear Lie algebra in dimension 2
  Problem Set 5 due in lecture.
  
  
• Monday, October 6
  Representations of the special linear Lie algebra in dimension 3, Part I
  
  
  
• Wednesday, October 8
  Representations of the special linear Lie algebra in dimension 3, Part II
  Problem Set 6 due in lecture.
  
  
• Monday, October 13
  NO LECTURE
  
  
• Wednesday, October 15
  The general setup: analyzing the structure and representations of an arbitrary semisimple Lie algebra
  Problem Set 7 due in lecture.
  
  
• Monday, October 20
  The special linear Lie algebras
  
  
• Wednesday, October 22
  Symplectic Lie algebras, Part I
  Problem Set 8 due in lecture.
  
  
• Monday, October 27
  Symplectic Lie algebras, Part II
  
  
• Wednesday, October 29
  Orthogonal Lie algebras, Part I
  Problem Set 9 due in lecture.
  
  
• Monday, November 3
  Orthogonal Lie algebras, Part II
  
  
• Wednesday, November 5
  Spin representations
  Problem Set 10 due in lecture.
  
  
• Monday, November 10
  The classification of complex simple Lie algebras
  
  
• Wednesday, November 12
  The exceptional Lie algebras
  Problem Set 11 due in lecture.
  
  
• Monday, November 17
  Complex Lie groups and characters
  
  
• Wednesday, November 19
  The Weyl character formula
  Problem Set 12 due in lecture.
  
  
• Monday, November 24
  More character formulas
  
  
• Wednesday, November 26
  NO LECTURE
  
  
  
• Monday, December 1
  Real Lie algebras and Lie groups
  
  
• Wednesday, December 3
  Additional topics
  Problem Set 13 due in lecture.
  
  

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