Speaker: Leonid Rybnikov (HSE, Moscow)

Date and time: 16.09.2020, 17:00 (GMT +03:00)

Title: Quantization of Drinfeld zastava spaces

Abstract: Drinfeld zastava is a certain closure of the moduli space of based maps from the projective line to the flag variety of the Lie algebra sl_n (also known as the monopole space). The natural (Atiyah-Hitchin) Poisson structure on the space of maps extends to the zastava space. We describe it in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian reduction of the corresponding quotient of its universal enveloping algebra produces a quantization Y of the coordinate ring of the zastava space . The same quantization was obtained by Gerasimov, Kharchev, Lebedev and Oblezin in 2004 as a subquotient of the Yangian Y(gl_n). We also generalize our construction to the case of the affine Kac-Moody algebra sl_n^.

(The talk  is based on the joint work with Michael Finkelberg arXiv:1009.0676)

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com