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Showing 1 to 7 of 7 for “"double affine"”.
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Double affine galleries
We develop a theory of galleries for double affine hyperplane arrangements. A gallery is an infinite sequence of chambers, indexed by an ordered set, which is maximal with respect to a finiteness condition on the multiset of wall-crossings. We study the possible order types of galleries. We also …
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Double Affine Bruhat Order
… with root system Phi_fin, one can create the affine Weyl group W_aff by taking the semidirect product of the translation group associated to the coroot lattice for Phi_fin, with W_fin. The double affine Weyl semigroup W can be created by using a similar semidirect product where one replaces …
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Double affine Hecke algebras and noncommutative geometry
In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the …
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On trigonometric and elliptic Cherednik algebras
… category of representations of the degenerate affine and double affine Hecke algebra of type BC. We also study the images of some D-modules and the principal series modules. In the second part, we define the elliptic Dunkl operators on an abelian variety with a finite group action. Using these …
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On conjectures related to character varieties of knots and Jones polynomials
… \ K) canonically becomes a module over a certain Double Affine Hecke Algebra, from which they defined a family of polynomials J_n(K; q; t_1; t_2) generalizing the classical polynomials of Jones. In this thesis an analogue of Habiro’s cyclotomic equation for the J_n(K; q) is discovered for J_n(K; …
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Quantized multiplicative quiver varieties and actions of higher genus braid groups
… of Dq-modules to representations of the type A double affine Hecke algebra of rank n. This functor is an instance of a more general construction which may be applied to any quasi-triangular Hopf algebra H, and yields representations of the elliptic braid group of rank n.
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Kauffman Bracket Skein Modules And The Quantum Torus
… The algebra Aq Z2 is the t = 1 subfamily of the double affine Hecke algebra Hq,t of type A1 . In Chapter 8 we give a new skein-theoretic realization of the + + spherical subalgebra Hq,t , and we also give a construction associating an Hq,t - module ML (t) to each knot L. In Chapter 9 we construct …