2 research outputs found
Macdonald operators and homological invariants of the colored Hopf link
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.Comment: 31 pages. Published version with an additional appendi