A Lax type operator for quantum finite W-algebras
A Lax type operator for quantum finite W-algebras
复制标题
量子有限W代数的Lax型算子
DOI：
10.1007/s00029-018-0439-6
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Daniele Valeri
中科院分区：
文献类型：
--
作者：
Alberto De Sole;V. Kac;Daniele Valeri
对于约化李代数及其幂零元f和忠实的有限维表示，我们构造了一个系数在量子有限W-代数中的Lax算子L（z）.我们证明了对于经典线性李代数，，和，算子L（z）满足一个广义Yangian恒等式。算子L（z）是我们最近在经典仿射系统中引入的广义Adler型算子的量子有限模拟。在后一种情况下，L（z）作为广义拟行列式得到。
For a reductive Lie algebra, its nilpotent elementfand its faithful finite dimensional representation, we construct a Lax operatorL(z) with coefficients in the quantum finiteW-algebra. We show that for the classical linear Lie algebras,,and, the operatorL(z) satisfies a generalized Yangian identity. The operatorL(z) is a quantum finite analogue of the operator of generalized Adler type which we recently introduced in the classical affine setup. As in the latter case,L(z) is obtained as a generalized quasideterminant.