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Matematicheskie Zametki, 2023, Volume 114, Issue 4, Pages 591–601
DOI: https://doi.org/10.4213/mzm13957
(Mi mzm13957)
 

On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups

Yu. A. Neretinabc

a University of Vienna
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
c Lomonosov Moscow State University
References:
Abstract: In the group algebra of the symmetric group $G=S_{n_1+\dots+n_\nu}$, we consider the subalgebra $\Delta$ consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup $H:=S_{n_1}\times \dots \times S_{n_\nu}$. We discuss structure constants of the algebra $\Delta$ and construct an algebra with continuous parameters $n_1,\dots,n_j$ extrapolating algebras $\Delta$, this can also be rewritten as an asymptotic algebra as $n_j\to\infty$ (for fixed $\nu$). We show that there is a natural map from the Lie algebra of the group of pure braids to $\Delta$ (and therefore this Lie algebra acts in spaces of multiplicities of the quasiregular representation of the group $G$ in functions on $G/H$).
Keywords: symmetric group, double cosets, Lie algebra of the group of braids, hypergeometric functions, Poisson algebra.
Funding agency Grant number
Austrian Science Fund P31591
The work is supported by FWF grant no. P31591.
Received: 22.03.2023
Revised: 23.04.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 4, Pages 583–592
DOI: https://doi.org/10.1134/S0001434623090262
Bibliographic databases:
Document Type: Article
UDC: 512.542.7+512.552.7+512.558.8
MSC: 20C30, 20N20, 33C20
Language: Russian
Citation: Yu. A. Neretin, “On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups”, Mat. Zametki, 114:4 (2023), 591–601; Math. Notes, 114:4 (2023), 583–592
Citation in format AMSBIB
\Bibitem{Ner23}
\by Yu.~A.~Neretin
\paper On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 4
\pages 591--601
\mathnet{http://mi.mathnet.ru/mzm13957}
\crossref{https://doi.org/10.4213/mzm13957}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 4
\pages 583--592
\crossref{https://doi.org/10.1134/S0001434623090262}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85174745271}
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