ct 2 00 9 Macdonald operators and homological invariants of the colored Hopf link
نویسنده
چکیده
Using a power sum (boson) realization for the Macdonald operators, we investigate Gukov, Iqbal, Kozçaz and Vafa’s 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.
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