Geodesic
Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Tome 481 (2019), pp. 29-38 
A. M. Vershik; N. V. Tsilevich. Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Tome 481 (2019), pp. 29-38. http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a2/
@article{ZNSL_2019_481_a2,
     author = {A. M. Vershik and N. V. Tsilevich},
     title = {Groups generated by involutions of diamond-shaped graphs, and deformations of {Young's} orthogonal form},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {29--38},
     year = {2019},
     volume = {481},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a2/}
}
TY  - JOUR
AU  - A. M. Vershik
AU  - N. V. Tsilevich
TI  - Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2019
SP  - 29
EP  - 38
VL  - 481
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a2/
LA  - ru
ID  - ZNSL_2019_481_a2
ER  - 
%0 Journal Article
%A A. M. Vershik
%A N. V. Tsilevich
%T Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 29-38
%V 481
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_481_a2/
%G ru
%F ZNSL_2019_481_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] G. Birkgof, Teoriya reshetok, Nauka, M., 1984 | MR

[2] J. D. Dixon, B. Mortimer, Permutation Groups, Springer, 1996 | MR | Zbl

[3] G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, 1981 | MR | Zbl

[4] S. V. Kerov, Asymptotic Representation Theory of the Symmetric Group and its Application in Analysis, Amer. Math. Soc., Providence, RI, 2003 | MR

[5] A. Okounkov, A. Vershik, “A new approach to representation theory of symmetric groups”, Selecta Math., New Series, 2:4 (1996), 581–605 | DOI | MR | Zbl

[6] R. Stenli, Perechislitelnaya kombinatorika, v. 1, Mir, M., 1990

[7] A. M. Vershik, “Avtomorfizm Paskalya imeet nepreryvnyi spektr”, Funkts. analiz i ego pril., 45:3 (2011), 16–33 | DOI | MR | Zbl

[8] A. M. Vershik, S. V. Kerov, “Lokalno poluprostye algebry. Kombinatornaya teoriya i $K_0$-funktor”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 26, 1985, 3–56 | Zbl

[9] A. M. Vershik, S. V. Kerov, “The Grothendieck group of the infinite symmetric group and symmetric functions (with the elements of the theory of $K_0$-functor of AF-algebras)”, Representation of Lie Groups and Related Topics, Adv. Stud. Contemp. Math., 7, eds. A. M. Vershik, D. P. Zhelobenko, Gordon and Breach, 1990, 39–117 | MR