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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2022

    a bare list of references, to be !included into the References-subsections of relevant entries

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2022
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022

    added previously missing pointer to this original reference:

    • Etsuro Date, Michio Jimbo, Atsushi Matsuo, Tetsuji Miwa, Hypergeometric-type integrals and the 𝔰𝔩(2,)\mathfrak{sl}(2,\mathbb{C})-Knizhnik-Zamolodchikov equation, International Journal of Modern Physics B 04 05 (1990) 1049-1057 [[doi:10.1142/S0217979290000528]]

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2022
    • (edited Jun 12th 2022)

    I have added the following pointers:


    Discussion for the special case of level=0=0 (cf. at logarithmic CFT – Examples):

    • Fedor A. Smirnov, Remarks on deformed and undeformed Knizhnik-Zamolodchikov equations, [[arXiv:hep-th/9210051]]

    • Fedor A. Smirnov, Form factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration, Communications in Mathematical Physics 155 (1993) 459–487 [[doi:10.1007/BF02096723]]

    • S. Pakuliak, A. Perelomov, Relation Between Hyperelliptic Integrals, Mod. Phys. Lett. 9 19 (1994) 1791-1798 [[doi:10.1142/S0217732394001647]]

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeJun 13th 2022

    In my memory, Varchenko’s book is not only a review, it has quite a few of new results and formulas (but I have to check when I will have time, now in the middle of a heavy exam grading season). Main emphasis in the book is on viewing hypergeometric pairing as relating quantum group (at root of unity) representations and affine Lie algebra representations. Regarding that there are some constructions (from the early days) of quantum groups from monodromies this is quite in accord with other intepretations,

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 13th 2022
    • (edited Jun 13th 2022)

    Yes, maybe. Though there is certainly a lot of review in the book, even an attempt to be expository.

    To some extent the book seems to be meant as filling in proofs that were left open in previous articles.

    Concretely, I was told that the book (i.e. Varchenko 1995) contains the proof of Feigin, Schechtman & Varchenko’s 1994 Remark 3.4.3 (the one on p. 10).

    But I haven’t found that proof yet. I have asked about it on MathOverflow (here), and others seem not to have found it either.

    But if anyone knows where the proof of that Remark 3.4.3 is spelled out “in print”, I’d be most grateful.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeJun 13th 2022

    I could ask somebody about it, I know somebody who traced their work when it was fresh.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 13th 2022

    I’d be interested in hearing what they may have to say!

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 19th 2022

    added pointer to:

    diff, v11, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2022

    added pointer to:

    • Atsushi Matsuo, An application of Aomoto-Gelfand hypergeometric functions to the SU(n)SU(n) Knizhnik-Zamolodchikov equation, Communications in Mathematical Physics 134 (1990) 65–77 [[doi:10.1007/BF02102089]]

    diff, v13, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeOct 22nd 2023
    • (edited Oct 22nd 2023)

    added pointer to:

    diff, v18, current