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nLab > Latest Changes: double affine Hecke algebra > history

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 27th 2023

    Mention the alternative name of Cherednik algebra and added redirects.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023
    • (edited Feb 2nd 2023)

    There is a major confusion here: there is an older entry on the same subject with more references double Hecke algebra, and then there is now this new stub about the same thing with, I think, misleading statement in the idea section. Affine is just a modifier for the emphasis, not for making a real distinction, unlike stated in the idea section.

    Double Hecke algebra and double affine Hecke algebra are the same notion and interchangeably called so by Cherednik, Ostrik, Etingof and others, DAHA being considered a more precise term.

    There are other variants though in generality. Ginzburg talks about symplectic reflection algebras which are more general than rational Cherednik algebras which are a special case.

    I suggest that we move the single new reference from the new entry into the bigger entry double Hecke algebra, make redirect or renaming for the integrated page or renaming if needed, and retire the new stub. I will be glad to do that if you agree. I would need to do significant amount of cross checking to be precise in the zoo of related notions.

    Also a number of meaningful related entries could be linked, like Dunkl operator, Calogero-Moser system, integrable system, spherical function etc.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Toward a more comprehensive idea section

    Double Hecke algebras or double affine Hecke algebras (DAHA) or Cherednik algebras are a particular class of multiparametric families of associative algebras; one parameter is q and then there are 1 or more parameters t α where labels α depend on a root system. While Iwahori-Hecke algebra is a deformation of the group algebra of a Weyl group, DAHA are flat deformations of certain crossed product algebras (or twisted group algebras) involving Coxeter groups. Affine denotes the relation to affine Weyl group in DAHA case. Ivan Cherednik introduced DAHA in proving Macdonald conjecture?s about orthogonal polynomials attached to reduced root systems.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Merging the two entries (in the process).

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Merging, second try in renaming

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Another try.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Another.

    diff, v3, current

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Another

    diff, v3, current

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

    Another.

    diff, v3, current

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2023

1 to 10 of 10

  1.