Séminaires : Séminaire d'Algèbre

The Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjecture) states that for any any given simple complex algebraic group G and any Poisson bracket from the Belavin-Drinfeld class, there exists a compatible generalized cluster structure. In this talk, I will review the process of constructing compatible generalized cluster structures, as well as the current state-of-the-art on the GSV conjecture. After that, I will describe a construction of generalized cluster structures on SL_n compatible with Poisson brackets induced from the Poisson dual of SL_n endowed with the Poisson structure determined by a BD triple of type A_{n-1}. I will also describe the associated family of birational quasi-isomorphisms. The talk will be based on the preprint arXiv:2312.04859 (joint work with M. Gekhtman). 

This talk will take place on Zoom only.