2014/05/08 by Byeong Hoon Kahng, Seok-Jin Kang, Kahng, Byeong Hoon +5 · 1 citation
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1405.1820
arxiv created 2014/05/08 · arxiv updated 2014/05/09
We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module Vq(λ) over a quantum generalized Kac-Moody algebra Uq(g) has a dual perfect basis and its dual perfect graph is isomorphic to the crystal B(λ). We also show that the negative half Uq-(g) has a dual perfect basis whose dual perfect graph is isomorphic to the crystal B(∞). More generally, we prove that all the dual perfect graphs of a given dual perfect space are isomorphic as abstract crystals. Finally, we show that the isomorphism classes of finitely generated graded projective indecomposable modules over a Khovanov-Lauda-Rouquier algebra and its cyclotomic quotients form dual perfect bases for their Grothendieck groups.