Introduction to DAHA in rank one (Ivan Cherednik, UNC Chapel Hill)

29.05.2019 14:00

Mostly in the case of root system A_1, we will
discuss the definition and some applications of DAHA, which is actually quite a ramified (but essentially elementary) theory by now even in the case of rank one. The key object will be the polynomial representation of DAHA and the action of PSL(2,Z) in this algebra. After the listeners become sufficiently familiar with the polynomial representation and Macdonald polynomials (Rogers’ ones for A_1) and their nonsymmetric generalizations (the first lecture), we will apply this to refined invariants of torus knotsand refined
Verlindealgebras(symmetric,nonsymmetric), including their q-deformations and non-semisimple Verlinde algebras, related to logarithmic CFT.
The third lecture will be actually sufficiently independent; we will review the necessary material from the first two.

Lieu

Bâtiment: Villa Battelle

Séminaire de la Tortue

entrée libre