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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 064, 34 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.064 (Mi sigma622) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Structure Constants of Diagonal Reduction Algebras of $\mathfrak{gl}$ Type

Sergei Khoroshkinab, Oleg Ogievetskycde

a Higher School of Economics, 20 Myasnitskaya Str., 101000 Moscow, Russia
b Institute of Theoretical and Experimental Physics, 117218 Moscow, Russia
c J.-V. Poncelet French-Russian Laboratory, UMI 2615 du CNRS, Independent University of Moscow, 11 B. Vlasievski per., 119002 Moscow, Russia
d Centre de Physique Théorique, Luminy, 13288 Marseille, France
e On leave of absence from P. N. Lebedev Physical Institute, Theoretical Department, 53 Leninsky Prospekt, 119991 Moscow, Russia
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DOI: https://doi.org/10.3842/SIGMA.2011.064
Abstract: We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\mathfrak{gl}_n$ into $\mathfrak{gl}_n\oplus\mathfrak{gl}_n$. Its representation theory is related to the theory of decompositions of tensor products of $\mathfrak{gl}$-modules.
Keywords: reduction algebra; extremal projector; Zhelobenko operators.
Received: January 14, 2011; in final form June 27, 2011; Published online July 9, 2011
Bibliographic databases:
Document Type: Article
MSC: 16S30; 17B35
Language: English
Citation: Sergei Khoroshkin, Oleg Ogievetsky, “Structure Constants of Diagonal Reduction Algebras of $\mathfrak{gl}$ Type”, SIGMA, 7 (2011), 064, 34 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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