2-Verma modules and the Khovanov-Rozansky link homologies
Abstract
We explain how Queffelec-Sartori's construction of the HOMFLY-PT link polynomial can be interpreted in terms of parabolic Verma modules for $\mathfrak{gl}_{2n}$. Lifting the construction to the world of categorification, we use parabolic 2-Verma modules to give a higher representation theory construction of Khovanov-Rozansky's triply graded link homology.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2017
- DOI:
- arXiv:
- arXiv:1704.08485
- Bibcode:
- 2017arXiv170408485N
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Geometric Topology;
- Mathematics - Representation Theory
- E-Print:
- v1, 32 pages, colored figures. v2, 42 pages, Proof of the main result expanded into a new subsection, minor corrections. v3, 24 pages. A gap in the proof of Theorem 4.9 (Dunfield-Gukov-Rasmussen conjecture) was found. As a consequence, it was removed and section 4.6 was substantially reduced. v4, 25 pages, peer reviewed version