Exotic cluster structures on SL_n

Seminar
Speaker
Alek Vainshtein (University of Haifa)
Date
29/04/2018 - 16:00 - 14:00Add to Calendar 2018-04-29 14:00:00 2018-04-29 16:00:00 Exotic cluster structures on SL_n Back in 2005, Berenstein, Fomin and Zelevinsky discovered a cluster structure in the ring of regular functions on a double Bruhat cell in a semisimple Lie group, in particular, SL_n. This structure can be easily extended to the whole group. The compatible Poisson bracket is given by the standard r-matrix Poisson-Lie structure on SL_n. The latter is a particular case of Poisson-Lie structures corresponding to quasi-triangular Lie bialgebras. Such structures where classified in 1982 by Belavin and Drinfeld. In 2012, we have conjectured that each Poisson-Lie structure on SL_n gives rise to a cluster structure, and gave several examples of exotic cluster structures corresponding to Poisson-Lie structures distinct from the standard one. In my talk I will tell about the progress in the proof of this conjecture and its modifications. Joint with M.Gekhtman and M.Shapiro.  Room 201 , Bldg 216 - Math and CS Building אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Room 201 , Bldg 216 - Math and CS Building
Abstract

Back in 2005, Berenstein, Fomin and Zelevinsky discovered a cluster
structure in the ring of regular functions on a double Bruhat cell in a
semisimple Lie group, in particular, SL_n. This structure can be easily
extended to the whole group. The compatible Poisson bracket is given by
the standard r-matrix Poisson-Lie structure on SL_n. The latter is a
particular case of Poisson-Lie structures corresponding to
quasi-triangular Lie bialgebras. Such structures where classified in 1982
by Belavin and Drinfeld. In 2012, we have conjectured that each
Poisson-Lie structure on SL_n gives rise to a cluster structure, and gave
several examples of exotic cluster structures corresponding to Poisson-Lie
structures distinct from the standard one. In my talk I will tell about the
progress in the proof of this conjecture and its modifications.

Joint with M.Gekhtman and M.Shapiro. 

Last Updated Date : 26/11/2019