2003/08/15 by Peter Magyar, Péter Magyar, Magyar, Peter
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0308156
17 pages. Minor revisions from v1. See also http://www.math.msu.edu/~magyar/
openalex publication_date 2003/08/15 · arxiv created 2003/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 E6, E7). 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.