Talk:Zonal spherical function
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Two mistakes in the section on the Harish-Chandra formula
[edit]K does not act on P by conjugation, and not every element of P is conjugate to A (e.g. a unipotent element cannot be conjugate to a semisimple element). ~2026-41074-10 (talk) 19:13, 23 July 2026 (UTC)
SL2R example.
[edit]I think there's a problem there. The article states that all zonal spherical functions are principal ones, but there are also the complementary ones (as is stated in the introduction). ~2026-41074-10 (talk) 20:38, 23 July 2026 (UTC)
Disputed status
[edit]Having noticed several inaccuracies (which I do not know personally how to best resolve) I flagged this for expert attention. Not being an expert myself, I suspect edits have been made be persons who are not necessarily experts in harmonic analysis.
A side note: should the page be called "zonal spherical function" or simply "spherical function"? Is the term "zonal" sufficiently well-established? I do not see it in any of the major textbooks I have consulted. ~2026-41074-10 (talk) 20:43, 23 July 2026 (UTC)
Another problem
[edit]I believe there is another problem: zonal spherical functions are described as the space of characters on the Hecke algebra. On the other hand, positive definiteness is taken to be a part of the definition of the zonal function. However, the space of such characters requires boundedness, but not positive-definiteness. ~2026-41074-10 (talk) 17:45, 24 July 2026 (UTC)
Background to the above problems
[edit]A substantial part of the content of this page (including the Harish—Chandra passage referred to above, which was added in this edit) was created by User:mathsci, who has since been banned indefinitely. The discussion about the ban (which centres on another article, double group) provides some insight into how these problems may have arisen (e.g.: “every other's edit of the article is either reverted or rewritten in his own style. If editors disagree, he continues an edit war until the other gives up” and “removing maintenance tags without addressing the issue”). I just thought I’d point that out to encourage people to be bold in trying to fix the problems. I unfortunately also lack the required expertise. Joriki (talk) 13:11, 29 July 2026 (UTC)