Geodesic
On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$
Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1375-1382 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the Lie algebra $\mathfrak g=\mathfrak{gl}(n,\mathbb C)$ it is proved that the maximal commutative subalgebras of the Poisson algebra $P(\mathfrak g)$ obtained by the method of shifting the invariants can be lifted to the enveloping algebra. Moreover, this lifting can be carried out by means of the symmetrization map. 
@article{SM_2000_191_9_a5,
     author = {A. A. Tarasov},
     title = {On some commutative subalgebras of the universal enveloping algebra of the {Lie} algebra $\mathfrak{gl}(n,\mathbb C)$},
     journal = {Sbornik. Mathematics},
     pages = {1375--1382},
     year = {2000},
     volume = {191},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_9_a5/}
}
TY  - JOUR
AU  - A. A. Tarasov
TI  - On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 1375
EP  - 1382
VL  - 191
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_9_a5/
LA  - en
ID  - SM_2000_191_9_a5
ER  - 
%0 Journal Article
%A A. A. Tarasov
%T On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$
%J Sbornik. Mathematics
%D 2000
%P 1375-1382
%V 191
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2000_191_9_a5/
%G en
%F SM_2000_191_9_a5
A. A. Tarasov. On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$. Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1375-1382. http://geodesic.mathdoc.fr/item/SM_2000_191_9_a5/

[1] Mischenko A. S., Fomenko A. T., “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 396–415 | MR | Zbl

[2] Vinberg E. B., “O nekotorykh kommutativnykh podalgebrakh universalnoi obertyvayuschei algebry”, Izv. AN SSSR. Ser. matem., 54:1 (1990), 3–25 | MR

[3] Nazarov M., Olshanski Gr., “Bethe subalgebras in twisted yangians”, Comm. Math. Phys., 178 (1996), 433–506 | DOI | MR

[4] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 55, VINITI, M., 1989, 137–309 | MR