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Joint IRT/Combinatorics Colloquium: New generalized cluster structures on GL(n) - a case study
Event Type
Seminar/Symposium
Sponsor
IRT seminar
Location
345 Altgeld Hall
Date
Feb 6, 2025 4:00 pm
Speaker
Michael Gekhtman
Contact
Trung Vu
E-Mail
hvu@illinois.edu
Views
13
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.
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