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Zap. Nauchn. Sem. POMI, 2019, Volume 481, Pages 29–38 (Mi znsl6786)  

This article is cited in 1 scientific paper (total in 1 paper)

Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form

A. M. Vershikabc, N. V. Tsilevichba

a Saint Petersburg State University
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

Abstract: With an arbitrary finite graph having a special form of 2-intervals (a diamond-shaped graph) we associate a subgroup of a symmetric group and a representation of this subgroup; state a series of problems on such groups and their representations; and present results of some computer simulations. The case we are most interested in is that of the Young graph and subgroups generated by natural involutions of Young tableaux. In particular, the classical Young orthogonal form can be regarded as a deformation of our construction. We also state asymptotic problems for infinite groups.

Key words and phrases: permutation groups, graded graphs, combinatorial involutions, symmetric group.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00433_а
Partially supported by the RFBR grant 17-01-00433.


Full text: PDF file (199 kB)
References: PDF file   HTML file
UDC: 512.542.7, 512.547
Received: 21.10.2019

Citation: A. M. Vershik, N. V. Tsilevich, “Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Zap. Nauchn. Sem. POMI, 481, POMI, St. Petersburg, 2019, 29–38

Citation in format AMSBIB
\Bibitem{VerTsi19}
\by A.~M.~Vershik, N.~V.~Tsilevich
\paper Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XXX
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 481
\pages 29--38
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6786}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, “Kombinatornoe kodirovanie skhem Bernulli i asimptotika tablits Yunga”, Funkts. analiz i ego pril., 54:2 (2020), 3–24  mathnet  crossref
  • Записки научных семинаров ПОМИ
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