2009/10/31 by Hidetoshi Awata, Hiroaki Kanno · 1 citation
Mathematics · Physics and Astronomy · #math.QA #hep-th #math.GT #msc:05A30 #msc:33D52 #msc:57M27 #msc:81T45
paper · pdf · doi:10.1088/1751-8113/44/37/375201
published as J.Phys.A44:375201,2011 · 31 pages. Published version with an additional appendix
arxiv created 2011/08/30 · arxiv updated 2011/08/31
Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers.