Littelmann's path model gives a flexible way to construct the
crystal graph of any irreducible representation of a Kac-Moody algebra:
almost all the known generalizations of Young tableaux can be derived from
We focus on the case of an affine Lie algebra g-hat and its basic
representation V(Lam_0). When the underlying finite-dimensional algebra g
is of classical type, the Kyoto school has given a model for the crystal
graph in terms of certain infinite paths. We unify this picture with
Littelmann's finite paths, and extend the Kyoto model to g = E_6 and E_7:
namely to all those g which admit a minuscule representation.
Our model gives a combinatorial explanation of the "Tensor Product
Phenomenon": The g-hat module V(Lam_0), when considered as a g-module, is
isomorphic to an infinite tensor product of small representations of g.
The above talk will be preceded by a VIGRE pre-talk, also by Peter Magyar,
to be held from 3:15-3:45pm in 3866 East Hall, i.e. the regular
seminar room. The topic of the pre-talk is:The Littelmann Path Model