Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 27 mars 2018 à 14h00 en B107, Gleb Koshevoy nous parlera de : Cluster relations among Schur functions and a positivity conjecture

Résumé : Cluster algebras, invented by Sergey Fomin and Andrei Zelevinsky around 2000, are commutative algebras whose generators and relations are constructed in a recursive manner. Due to cluster recursion we obtain Laurent polynomials in the initial variables, so-called Laurent phenomenon of cluster algebras. The coordinate ring of base affine space C[N_-\SL_n] plays an important role in representation theory and is endowed with a cluster algebra structure. We show that under specialization of minors to Schur functions, Laurent polynomials of this cluster algebra turn into 'homogeneous' sums of Schur function. A positivity conjecture says that these sums have positive coefficients. This conjecture is true for finite cluster subalgebras.


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