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From crystal bases to geometric crystals

SPEAKER: Arkady Berenstein

TITLE: From crystal bases to geometric crystals.

ABSTRACT The goal of my talk is to construct crystal bases (for irreducible modules over semisimple Lie algebras) by means of geometric crystals. Geometric and unipotent crystals have been introduced a few years ago in a joint work with David Kazhdan as a useful geometric version of Kashiwara crystals. More recent observations show that geometric crystals provide families of piecewise-linear parametrizations of crystal bases and reveal such hidden combinatorial structures as ‘crystal multiplication’ and ‘central charge’ on tensor products of crystal bases.