Introduction to quantum groups. 2020

Plan of the course.
  1. Poisson algebras and quantization. Notes.
  2. Poisson-Lie groups and Lie bialgebras. Notes.
  3. Dual Poisson-Lie groups, symplectic leaves. Notes.
  4. Classical r-matrix. Notes.
  5. Quantum groups and algebras. Example of sl(2). Notes.
  6. Hopf algebras. Notes.
  7. Quantum R-matrix.Notes.
  8. Drinfeld-Jimbo quantum groups. Notes.
  9. RTT realization. Notes.
  10. Function on quantum SL(2). Notes.
  11. Function on quantum SL(n). Notes.
  12. Lusztig's group. Notes.
  13. Universal R-matrix. Notes.
  14. Drinfeld double. Notes.

Problems.

Recordings of the lectures. playlist.

Affine quantum groups. 2021

Plan of the course.
  1. Quantum groups (quick review). Notes
  2. Affine Lie algebras, affine Weyl groups Notes.
  3. Affine Lie algebras, representations.
  4. Affine quantum sl(2), PBW generators. Notes.
  5. Affine quantum sl(2), new Drinfeld realization. Notes
  6. Factorization of R matrix. Notes.
  7. RLL realization for affine sl(2). Notes
  8. Finite dimensional representations of affine sl(2). Notes.
  9. q-characters for affine sl(2). Notes.
  10. q-characters Notes.
  11. Schur-Weyl duality. Hecke algebras. Notes.
  12. Semi-infinite construction Notes.
  13. Bosonization, vertex operators Notes.
  14. Baxter subalgebras, XXZ model. KZ integrals. Bether ansantz.
  15. q-characters from Baxter subalgebras. TQ relations.

Problems.

Recordings of the lectures. playlist.

Introduction to quantum groups. 2023

Plan of the course.
  1. Poisson algebras and quantization. Notes.
  2. Poisson-Lie groups and Lie bialgebras. Notes.
  3. Classical r-matrices. Notes.
  4. Dual Poisson-Lie groups, symplectic leaves. Notes.
  5. Quantum groups and algebras. Example of sl(2). Notes.
  6. Hopf algebras. Notes.
  7. Quantum R-matrices.Notes.
  8. Drinfeld-Jimbo quantum groups. Notes.
  9. Finite dimensional Representation of Uq(g). Notes.
  10. Drinfeld double. Drinfeld theorem. Notes.
  11. RTT realization. Notes.
  12. Functions on quantum SL(2). Notes.
  13. Functions on quantum SL(n). Notes.
  14. Lusztig's group. Notes.
  15. Factorization of universal R matrix . Notes.

Problems.

Recordings of the lectures. playlist.