Sergei Khoroshkin, Oleg Ogievetsky, “Structure Constants of Diagonal Reduction Algebras of $\mathfrak{gl}$ Type”, SIGMA, 2011, том 7,064, 34 стр.

Эта публикация цитируется в 4 статьях

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

Sergei Khoroshkin^ab, Oleg Ogievetsky^cde

^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

Аннотация: 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.

Ключевые слова: reduction algebra; extremal projector; Zhelobenko operators.

MSC: 16S30; 17B35

Поступила: 14 января 2011 г.; в окончательном варианте 27 июня 2011 г.; опубликована 9 июля 2011 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2011.064