Refined composite invariants of torus knots via DAHA
Abstract
We define composite DAHA-superpolynomials of torus knots, depending on pairs of Young diagrams and generalizing the composite HOMFLY-PT polynomials in the theory of the skein of the annulus. We provide various examples. Our superpolynomials extend the DAHA-Jones (refined) polynomials and satisfy all standard symmetries of the DAHA-superpolynomials of torus knots. The latter are conjecturally related to the HOMFLY-PT homology; such a connection is a challenge in the theory of the annulus. At the end, we construct two DAHA-hyperpolynomials extending the DAHA-Jones polynomials of type E and closely related to the exceptional Deligne-Gross series of root systems; this theme is of experimental nature.
Keywords
Cite
@article{arxiv.1503.01441,
title = {Refined composite invariants of torus knots via DAHA},
author = {Ivan Cherednik and Ross Elliot},
journal= {arXiv preprint arXiv:1503.01441},
year = {2015}
}
Comments
v2: 3 references were added and minor editing