1999/01/31 by Goro Hatayama, Yoshiyuki Koga, Atsuo Kuniba +2
Mathematics · Physics and Astronomy · #math.QA #hep-th #math-ph #math.MP #msc:81R10
published as Advanced Studies in Pure Mathematics 28(2000) 113-132 · 15 pages, LaTeX2e, submitted to the proceedings of the RIMS98 program "Combinatorial Methods in Representation Theory"
arxiv created 1999/02/10 · arxiv updated 2009/11/30
We consider a category of finite crystals of a quantum affine algebra whose objects are not necessarily perfect, and set of paths, semi-infinite tensor product of an object of this category with a certain boundary condition. It is shown that the set of paths is isomorphic to a direct sum of infinitely many, in general, crystals of integrable highest weight modules. We present examples from Cn(1) and An-1(1), in which the direct sum becomes a tensor product as suggested from the Bethe Ansatz.