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From geometric crystals to crystal bases

Berenstein, A (Oregon)
Tuesday 31 March 2009, 09:30-10:15



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 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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