42 research outputs found
Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0
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
Crystal bases for quantum affine algebras and Young walls
AbstractWe provide a unified approach to the Young wall description of crystal graphs for arbitrary level irreducible highest weight representations over classical quantum affine algebras. The crystal graph is realized as the affine crystal consisting of all reduced Young walls built on a ground-state wall
Young Wall Realization of Crystal Bases for Classical Lie Algebras
In this paper, we give a new realization of crystal bases for finite
dimensional irreducible modules over classical Lie algebras. The basis vectors
are parameterized by certain Young walls lying between highest weight and
lowest weight vectors.Comment: 27page