Geometric crystals, potentials, and tropicalization (Arkady Berenstein, University of Oregon)

05.12.2017 15:30

The goal of my talk is to construct Kashiwara crystal bases for simple G^\vee-modules by means of a geometric crystal on the basic affine space G/U (here G is a reductive algebraic group, U is its maximal unipotent subgroup, and G^\vee is the Langlands dual group of G). The construction includes certain potential on G/U, which is also instrumental in Mirror Symmetry, and its tropicalization with respect to an appropriate positive structure on G/U.

Geometric and unipotent crystals were introduced in my joint work with David Kazhdan in 2000 as a useful geometric analogue of Kashiwara crystals. Recent observations show that geometric crystals,in addition to providing families of piecewise-linear parameterizations of crystal bases, also reveal such hidden combinatorial structures as "crystal multiplication" and "central charge" of tensor products of Kashiwara crystal bases.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre