43 research outputs found
Classical Limit of genus two DAHA
We show that one-parameter deformation of the skein
algebra of a genus two surface suggested in [AS19] is flat. We
solve the word problem in the algebra and describe monomial basis. In addition,
we calculate the classical limit of the algebra and prove
that it is a one-parameter flat Poisson deformation of the coordinate ring
of an -charater variety of a genus two
surface. As a byproduct, we obtain a remarkably simple presentation in terms of
generators and relations for the coordinate ring of a
genus two character variety.Comment: 36 pages, 1 figur
An Elliptic Generalization of Spherical DAHA at
We construct an algebra that is an elliptic generalization of spherical
DAHA acting on its finite-dimensional module at with . We
prove that acts by automorphisms of the algebra we
constructed, and provide an explicit representation of automorphisms and
algebra operators alike by matrices of elliptic functions. A
relation of this construction to the K-theory character of affine Laumon space
is conjectured. We point out two potential applications, respectively to
symmetry of Felder-Varchenko functions and to new elliptic
invariants of torus knots and Seifert manifolds.Comment: 32 page
Link polynomial calculus and the AENV conjecture
Using the recently proposed differential hierarchy (Z-expansion) technique,
we obtain a general expression for the HOMFLY polynomials in two arbitrary
symmetric representations of link families, including Whitehead and Borromean
links. Among other things, this allows us to check and confirm the recent
conjecture of arXiv:1304.5778 that the large representation limit (the same as
considered in the knot volume conjecture) of this quantity matches the
prediction from mirror symmetry consideration. We also provide, using the
evolution method, the HOMFLY polynomial in two arbitrary symmetric
representations for an arbitrary member of the one-parametric family of
2-component 3-strand links, which includes the Hopf and Whitehead links.Comment: 20 page