2009/09/30 by Aaron D. Lauda, Monica Vazirani · 1 citation
Mathematics · #math.RT #msc:81R50 #msc:05E10 #msc:20C08 #msc:17B37
paper · pdf · doi:10.1016/j.aim.2011.06.009
published as Advances in Mathematics, Volume 228, Issue 2, 1 October 2011, Pages 803-861 · 56 pages, 6 eps files. v2 corrects typos
arxiv created 2011/05/03 · arxiv updated 2011/08/02
We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group.