A NON-LOCAL POISSON BRACKET FOR COXETER-TODA LATTICES

Autor(es)

Chuno, Eber

• Tipo de documento: Artigo Científico
• Fonte: Colloquium Mathematicum; v. 161, n. 1, p. 22-pg., 2020-01-01.

Resumo

We present a non-local Poisson bracket defined on the phase space G(u,v)/H, where G(u,v) is a Coxeter double Bruhat cell of GL(n) and H is the subgroup of diagonal matrices. The non-local Poisson bracket is written in an appropriate set of coordinates of G(u,v)/H derived from a set of factorization parameters for G(u,v). We show that the non-local Poisson bracket corresponds to the Atiyah-Hitchin bracket under the Moser map. As a consequence, the non-local Poisson bracket is compatible with a quadratic Poisson bracket obtained by M. Gekhtman, M. Shapiro and A. Vainshtein (2011). (AU)

• Processo FAPESP: 14/08512-3 - Cluster álgebras e sistemas integráveis
• Beneficiário: Eber Daniel Chuno Vizarreta
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado