43 citations · 87 across the 12 of their papers we have counts for
14 papers
The Temperley-Lieb Tower and the Weyl Algebra
Matthew Harper, Peter Samuelson
We define a monoidal category and a closely related 2-category using diagrammatic methods. We show that $\operatorname{\…
On the genus two skein algebra
Juliet Cooke, Peter Samuelson
We study the skein algebra of the genus 2 surface and its action on the skein module of the genus 2 handlebody. We compute this action explicitly, and we describe how the module de…
DAHAs and skein theory
Hugh Morton, Peter Samuelson
We give a skein-theoretic realization of the double affine Hecke algebra of Cherednik using braids and tangles in the punctured torus. We use this to provide evid…
The Kauffman skein algebra of the torus
Hugh Morton, Alexander Pokorny, Peter Samuelson
We give a presentation of the Kauffman (BMW) skein algebra of the torus, which is the "type BCD" analogue of the Homflypt skein algebra of torus which was computed by the first and…
Cyclotomic Expansion of Generalized Jones Polynomials
Yuri Berest, Joseph Gallagher, Peter Samuelson
In previous work of the first and third authors, we proposed a conjecture that the Kauffman bracket skein module of any knot in carries a natural action of the rank 1 double…
The Hall Algebras of Annuli
Benjamin Cooper, Peter Samuelson
We refine and prove the central conjecture of our first paper for annuli with at least two marked intervals on each boundary component by computing the derived Hall algebras of the…
The Hall Algebras of Surfaces I
Benjamin Cooper, Peter Samuelson
We study the derived Hall algebra of the partially wrapped Fukaya category of a surface. We give an explicit description of the Hall algebra for the disk with m marked intervals an…
Affine cubic surfaces and character varieties of knots
Yuri Berest, Peter Samuelson
It is known that the fundamental group homomorphism induced by the inclusion of the boundary torus into the complement of a knot in is…
The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
Sabin Cautis, Aaron D. Lauda, Anthony Licata +2
We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined by Licata and Savage. We also show that as an algebra, it is isomor…
The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra
Hugh Morton, Peter Samuelson
We give a generators and relations presentation of the HOMFLYPT skein algebra of the torus , and we give an explicit description of the module corresponding to the solid t…
Iterated torus knots and double affine Hecke algebras
Peter Samuelson
We give a topological realization of the (spherical) double affine Hecke algebra of type , and we use this to construct a module over f…
Double affine Hecke algebras and generalized Jones polynomials
Yuri Berest, Peter Samuelson
In this paper, we propose and discuss implications of a general conjecture that there is a canonical action of a rank 1 double affine Hecke algebra on the Kauffman bracket skein mo…
Dunkl Operators and Quasi-invariants of Complex Reflection Groups
Yuri Berest, Peter Samuelson
These are lecture notes of a minicourse given by the first author at the Summer School on Quantization at the University of Notre Dame in June 2011. The notes were written up and e…
Character algebras of decorated SL_2(C)-local systems
Greg Muller, Peter Samuelson
Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S,…