Projects per year
Abstract
We give a topological realization of the (spherical) double affine Hecke algebra SHq,t of type sl2, and we use this to construct a module over SHq,t for any knot K⊂S3 . As an application, we give a purely topological interpretation of Cherednik's 2-variable polynomials Pn (r,s;q,t) of type sl2 from [Che13] (where r,s ∈ Z are relatively prime), and we give a new proof that these specialize to the colored Jones polynomials of the r,s
torus knot.
We then generalize Cherednik's construction (for sl2 ) to all iterated cables of the unknot and prove the corresponding specialization property. Finally, in the appendix we compare our polynomials associated to iterated torus knots to the ones recently defined in [CD14], in the specialization t=−q 2 .
We then generalize Cherednik's construction (for sl2 ) to all iterated cables of the unknot and prove the corresponding specialization property. Finally, in the appendix we compare our polynomials associated to iterated torus knots to the ones recently defined in [CD14], in the specialization t=−q 2 .
Original language | English |
---|---|
Pages (from-to) | 2848–2893 |
Number of pages | 28 |
Journal | International Mathematics Research Notices |
Volume | 2019 |
Issue number | 9 |
DOIs | |
Publication status | Published - 4 Sept 2017 |
Fingerprint
Dive into the research topics of 'Iterated torus knots and double affine Hecke algebras'. Together they form a unique fingerprint.Projects
- 1 Finished
-
QuantGeomLangTFT - The Quantum Geometric Langlands Topological Field Theory
Jordan, D. (Principal Investigator)
1/06/15 → 31/05/21
Project: Research