Math 607 WINTER 2014, List of lectures

  • On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.
  • Monday, January 6: The Witt algebra. (One dimensional) central extensions of Lie algebras. Here is homework!
  • Wednesday, January 8: Theorem: H^2(W)=C. The Virasoro algebra. Other examples: Heisenberg (or oscillator) and affine Lie algebras.
  • Friday, January 10: Positive energy representations. Unitary representations.
  • Monday, January 13: Fock spaces as representations of Heisenberg algebra.
  • Wednesday, January 15: Virasoro algebra action on the Fock spaces.
  • Friday, January 17: Highest weight representations of the Virasoro algebra. Existence of Hermitian contravariant form. New homework!
  • Wednesday, January 22: Unitary representations of Virasoro algebra from deformed action on the Fock space and from the fermions.
  • Friday, January 24: Kac determinant. Some non-unitary representations.
  • Monday, January 27: Divisibility properties of Kac determinant.
  • Wednesday, January 29: Degree of Kac determinant. Relations in loop algebra of sl(2).
  • Friday, January 31: Contragredient Lie algebras and Kac-Moody Lie algebras.
  • Monday, February 3: Kac-Moody Lie algebras are integrable.
  • Wednesday, February 5: Affine Lie algebras as Kac-Moody algebras.
  • Friday, February 7: Class was cancelled.
  • Monday, February 10: Highest weight representations. Integrable representations and Weyl group.
  • Wednesday, February 12: Weyl-Kac character formula and denominator identity.
  • Friday, February 14: Invariant bilinear form.
  • Monday, February 17: Casimir operator.
  • Wednesday, February 19: Proof of Weyl-Kac formula. New (incomplete) homework!
  • Friday, February 21: Characters for affine sl(2) and theta functions. Heisenberg subalgebra and basic representation.
  • Monday, February 24: Vertex operator construction of basic module for affine sl(2).
  • Wednesday, February 26: Unitarity of integrable highest weight representations of affine sl(2). Updated homework!
  • Friday, February 28: Affine and Virasoro Lie algebras: Sugawara construction.
  • Monday, March 3: Coset construction.
  • Wednesday, March 5: Singular vectors for Verma modules over Virasoro algebra.
  • Friday, March 7: Quantum fields and locality. Vertex algebras.
  • Monday, March 10: More of vertex algebras
  • Wednesday, March 12: Conformal blocks.
  • Friday, March 14: Tensor categories.