1999/06/15 by Toshiki Nakashima, Nakashima, Toshiki
Mathematics · #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/9906100
LaTeX(2e), 19 pages
arxiv created 1999/06/15 · arxiv updated 2009/11/30
We review the polyhedral realizations of crystal bases in the former half and in the latter half, we introduce braid-type isomorphisms for some rank 2 finite type crystals. Using this isomorphisms, for semi-simple Lie algebra we can show that polyhedral realizations can be obtained in the lattice of finite rank which coincides with the length of the longest element in the associated Weyl group.