On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 185-200 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The asymptotics of multiplicities of irreducible representations in large tensor products of finite dimensional representations of simple Lie algebras are computed for all, including nongeneric, highest weights.
@article{ZNSL_2021_509_a11,
     author = {O. V. Postnova and N. Yu. Reshetikhin},
     title = {On the asymptotics of multiplicities for large tensor product of representations of simple {Lie} algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {185--200},
     year = {2021},
     volume = {509},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a11/}
}
TY  - JOUR
AU  - O. V. Postnova
AU  - N. Yu. Reshetikhin
TI  - On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 185
EP  - 200
VL  - 509
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a11/
LA  - en
ID  - ZNSL_2021_509_a11
ER  - 
%0 Journal Article
%A O. V. Postnova
%A N. Yu. Reshetikhin
%T On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 185-200
%V 509
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a11/
%G en
%F ZNSL_2021_509_a11
O. V. Postnova; N. Yu. Reshetikhin. On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 185-200. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a11/

[1] Ph. Biane, “Estimation asymptotique des multiplicites dans les puissances tensorielles d'un $\mathfrak{g}$-module”, C.R. Acad. Sci. Paris, Serie I, 316, 849–852 | MR | Zbl

[2] E. Feigin, “Large tensor products and Littlewood–Richardson coefficients”, J. Lie Theory, 29:4 (2019), 927–940 | MR | Zbl

[3] S. Kerov, “On asymptotic distribution of symmetry types of high rank tensors”, Zap. Nauchn. Semin. POMI, 155, 1986, 181–186 | Zbl

[4] S. Kerov, Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis, Translations of Mathematical Monographs, 219, 2003 | DOI | Zbl

[5] B. Logan, L. Shepp, “A variational problem for random Young tableaux”, Advances in Mathematics, 26:2 (1977), 206–222 | DOI | MR | Zbl

[6] A. Nazarov, O. Postnova, “The limit shape of a probability measure on a tensor product of modules on the $B_n$ algebra”, Zap. Nauchn. Semin. POMI, 468, 2018, 82–97

[7] O. Postnova, N. Reshetikhin, “On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras”, Letters Math. Phys. Serie I, 110 (2020) | MR | Zbl

[8] O. Postnova, N. Reshetikhin, V. Serganova, On character measure in large tensor product of representations of simple Lie algebras and superalgebras, TBA

[9] T. Tate, S. Zelditch, “Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers”, J. Funct. Anal., 217:2 (2004), 402–447 | DOI | MR | Zbl

[10] A. Vershik, S. Kerov, “Asymptotics of Plancherel measure of symmetrical group and limit form of young tables”, Dokl. Akad. Nauk SSSR, 233:6 (1977), 1024–1027 | MR | Zbl

[11] A. Vershik, S. Kerov, “Asymptotic of the largest and the typical dimensions of irreducible representations of a symmetric group”, Funct. Analysis Its Appl., 19:1 (1985), 21–31 | DOI | Zbl

[12] A. Vershik (Ed.), A European Mathematical Summer School held at the Euler Institute (St. Petersburg, Russia, July 9–20, 2001), Lecture Notes in Mathematics, 1815