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arXiv · 0910.0083

Macdonald operators and homological invariants of the colored Hopf link

Hidetoshi Awata·Hiroaki Kanno
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Abstract

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.

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BibTeXRIS

Hidetoshi Awata, Hiroaki Kanno. 2009-10-01. Macdonald operators and homological invariants of the colored Hopf link. https://doi.org/10.1088/1751-8113/44/37/375201

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