From geometric crystals to crystal bases
AbstractThe 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 analogue of Kashiwara crystals. More recent observations (based on the recent joint paper with David Kazhdan) show that geometric crystals, in addition to providing families of piecewise-linear parametrizations of crystal bases, also reveal such hidden combinatorial structures as 'crystal multiplication' and 'central charge' on tensor products of crystal bases.
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