Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: double affine Hecke algebra

Bottom of Page

1 to 4 of 4

  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Double Hecke algebras or double affine Hecke algebras (DAHA) or __Cherednik algebra__s are a particular class of 2-parametric families of associative algebras. These families are flat deformations of certain crossed product algebras involving Coxeter groups. Ivan Cherednik introduced DAHA in proving Macdonald conjectures about orthogonal polynomials attached to reduced root systems.

    diff, v7, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Integrated page.

    diff, v7, current

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023
    • (edited Feb 2nd 2023)

    I should add the following remark to our discussion in the other thread: while there is no standard mathematical difference in saying double Hecke algebra versus double affine Hecke algebra there is of course a difference between saying Hecke algebra and affine Hecke algebra. The latter maybe deserves a new entry.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeFeb 3rd 2023
    • (edited Feb 3rd 2023)

    Notice that rational Cherednik algebras defined by Etingof and Ginzburg are not literally DAHAs, but certain degenerations of those and can be considered a special case of symplectic reflection algebras.

    diff, v8, current

    Edit: for this reason I have moved some of the references into the new entry rational Cherednik algebra.

1 to 4 of 4

  1.