SIGMA 7 (2011), 064, 34 pages      arXiv:1101.2647      https://doi.org/10.3842/SIGMA.2011.064

Structure Constants of Diagonal Reduction Algebras of gl Type

Sergei Khoroshkin ^{a, b} and Oleg Ogievetsky ^{c, d, e
a)} Institute of Theoretical and Experimental Physics, 117218 Moscow, Russia
^b) Higher School of Economics, 20 Myasnitskaya Str., 101000 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

Received January 14, 2011, in final form June 27, 2011; Published online July 09, 2011

Abstract
We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra gl_n into gl_n⊕gl_n. Its representation theory is related to the theory of decompositions of tensor products of gl_n-modules.

Key words: reduction algebra; extremal projector; Zhelobenko operators.

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References

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