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Mat. Sb., 2000, Volume 191, Number 9, Pages 115–122 (Mi msb509)  

This article is cited in 11 scientific papers (total in 11 papers)

On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$

A. A. Tarasov

M. V. Lomonosov Moscow State University

Abstract: 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.

DOI: https://doi.org/10.4213/sm509

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English version:
Sbornik: Mathematics, 2000, 191:9, 1375–1382

Bibliographic databases:

UDC: 519.46
MSC: Primary 17B35; Secondary 16S30, 17B45, 17B63
Received: 13.10.1999

Citation: A. A. Tarasov, “On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$”, Mat. Sb., 191:9 (2000), 115–122; Sb. Math., 191:9 (2000), 1375–1382

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Tarasov, “Uniqueness of liftings of maximal commutative subalgebras of the Poisson–Lie algebra to the enveloping algebra”, Sb. Math., 194:7 (2003), 1105–1111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. L. G. Rybnikov, “Centralizers of certain quadratic elements in Poisson–Lie algebras and the method of translation of invariants”, Russian Math. Surveys, 60:2 (2005), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. L. G. Rybnikov, “The Argument Shift Method and the Gaudin Model”, Funct. Anal. Appl., 40:3 (2006), 188–199  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. M Jimbo, H Nagoya, J Sun, “Remarks on the confluent KZ equation for \mathfrak{sl}_2 and quantum Painlevé equations”, J Phys A Math Theor, 41:17 (2008), 175205  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Feigin, B, “Gaudin models with irregular singularities”, Advances in Mathematics, 223:3 (2010), 873  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Feigin B., Frenkel E., “Quantization of Soliton Systems and Langlands Duality”, Exploring New Structures and Natural Constructions in Mathematical Physics, Advanced Studies in Pure Mathematics, 61, eds. Hasegawa K., Hayashi T., Hosono S., Yamada Y., Math Soc Japan, 2011, 185–274  mathscinet  zmath  isi
    7. E. Mukhin, V. Tarasov, A. Varchenko, “Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra”, International Mathematics Research Notices, 2012  crossref  mathscinet  isi  scopus  scopus  scopus
    8. Futorny V., Molev A., “Quantization of the shift of argument subalgebras in type A”, Adv. Math., 285 (2015), 1358–1375  crossref  mathscinet  zmath  isi  scopus
    9. Alves I.Z.M. Petrogradsky V., “Lie Structure of Truncated Symmetric Poisson Algebras”, J. Algebra, 488 (2017), 244–281  crossref  mathscinet  zmath  isi  scopus
    10. Trans. Moscow Math. Soc., 78 (2017), 217–234  mathnet  crossref  elib
    11. Moreau A., “Centralizers of Nilpotent Elements and Related Problems, a Survey”, Perspectives in Lie Theory, Springer Indam Series, 19, eds. Callegaro F., Carnovale G., Caselli F., DeConcini C., DeSole A., Springer International Publishing Ag, 2017, 331–346  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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