Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 064, 34 pages      arXiv:1101.2647

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

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

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

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