Urbana Campus Research Calendar (OVCRI)

Joint IRT/Combinatorics Colloquium: New generalized cluster structures on GL(n) - a case study

Event Type

Seminar/Symposium

Sponsor

IRT seminar

Location

343 Altgeld Hall

Date

Feb 6, 2025   4:00 pm  

Speaker

Michael Gekhtman

Contact

Trung Vu

E-Mail

hvu@illinois.edu

Views

1

Originating Calendar

Integrability & Representation Theory (IRT) Seminar

I will discuss a generalized cluster on GL(n) compatible with the particular Poisson bracket that is homogeneous w.r.t. two-sided action of a Poisson-Lie group G=GL(n)xGL(n). Here the components  of G are equipped with two “opposite” versions of the Cremmer-Gervais Poisson-Lie bracket. Our construction relies on birational Poisson maps that relate the Poisson homogeneous structure under investigation with the phase space of the finite Toda lattice and the Poisson dual of the Cremmer-Gervais Poisson-Lie group. This is a joint work with M. Shapiro and A. Vainshtein.