Littelmann paths for the basic representation of an affine Lie algebra

Details Littelmann paths for the basic representation of an affine Lie algebra Littelmann paths for the basic representation of an affine Lie algebra

2003-08-15

arxiv.org/abs/math/0308156v2

Mathematics

Representation Theory

17 pages. Minor revisions from v1. See also http://www.math.msu.edu/~magyar/

Scientific paper

We give a new model for the crystal graphs of an affine Lie algebra g^, combining Littelmann's path model with the Kyoto path model. The vertices of the crystal graph are represented by certain infinitely looping paths which we call skeins. We apply this model to the case when the corresponding finite-dimensional algebra g has a minuscule representation (classical type and E_6, E_7). We prove that the basic level-one representation of g^, when considered as a representation of g, is an infinite tensor product of fundamental representations of g. A similar tensor product phenomenon holds for certain Demazure submodules of the basic representation.

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