Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0
Representation Theory
2008-11-26 v1 Quantum Algebra
Abstract
We present a uniform construction of level 1 perfect crystals for all affine Lie algebras. We also introduce the notion of a crystal algebra and give an explicit description of its multiplication. This allows us to determine the energy function on completely and thereby give a path realization of the basic representations at in the homogeneous picture.
Keywords
Cite
@article{arxiv.math/0507114,
title = {Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0},
author = {Georgia Benkart and Igor Frenkel and Seok-Jin Kang and Hyeonmi Lee},
journal= {arXiv preprint arXiv:math/0507114},
year = {2008}
}