Yangians and Mickelsson algebras II
Yangians and Mickelsson algebras II
复制标题
Yangians 和 Mickelsson 代数 II
DOI：
10.17323/1609-4514-2006-6-3-477-504
复制
发表时间：
2006
影响因子：
0.8
通讯作者：
M. Nazarov
中科院分区：
文献类型：
--
作者：
S. Khoroshkin;M. Nazarov
.我们研究两个函子的复合。第一个，从Lie代数gl m上的模范畴到GL N的退化Auredne Hecke代数上的模范畴，是由I. Cherednik引入的。第二个函子是V. Drinfeld的Yangian Y（gl n）上从后一个范畴到模范畴的函子的斜版本。给出了Y（gl n）-模的张量积上的交织算子与D. Zhelobenko引入的gl m的Weyl群上的“极值上循环”之间的联系的表示论解释.我们还建立了两个函子的合成之间的联系，和“中心化建设”的Yangian Y（gl n）的发现G. Olshanski。
. We study a composition of two functors. The first one, from the category of modules over the Lie algebra gl m to the category of modules over the degenerate affine Hecke algebra of GL N , was introduced by I.Cherednik. The second functor is a skew version of the functor from the latter category to the category of modules over the Yangian Y( gl n ) due to V.Drinfeld. We give a representation theoretic explanation of a link between intertwining operators on tensor products of Y( gl n )-modules, and the “extremal cocycle” on the Weyl group of gl m introduced by D.Zhelobenko. We also establish a connection between the composition of two functors, and the “centralizer construction” of the Yangian Y( gl n ) discovered by G.Olshanski.