Yangians and Mickelsson Algebras II

TY - JOUR

T1 - Yangians and Mickelsson Algebras II

AU - Khoroshkin, Sergey

AU - Nazarov, Maxim

PY - 2006/7

Y1 - 2006/7

N2 - We study the composition of two functors. The first functor, acting from the category of modules over the Lie algebra glm to the category of modules over the degenerate affine Hecke algebra of GLN, was introduced by Cherednik. The second functor is a skew version of the functor, due to Drinfeld, from the latter category to the category of modules over the Yangian Y(gln). We give a representation-theoretic explanation of a link between intertwining operators on tensor products of Y(gln)-modules and the “extremal cocycle” introduced by Zhelobenko on the Weyl group of glm. We also establish a connection between the composition of two functors and Olshanski's “centralizer construction” of the Yangian Y(gln).

AB - We study the composition of two functors. The first functor, acting from the category of modules over the Lie algebra glm to the category of modules over the degenerate affine Hecke algebra of GLN, was introduced by Cherednik. The second functor is a skew version of the functor, due to Drinfeld, from the latter category to the category of modules over the Yangian Y(gln). We give a representation-theoretic explanation of a link between intertwining operators on tensor products of Y(gln)-modules and the “extremal cocycle” introduced by Zhelobenko on the Weyl group of glm. We also establish a connection between the composition of two functors and Olshanski's “centralizer construction” of the Yangian Y(gln).

KW - Algebra;

KW - Pure Mathematics;

KW - Cherednik functor;

KW - Drinfeld functor;

KW - Zhelobenko cocycle

M3 - Article

SN - 1609-4514

VL - 6

SP - 477

EP - 504

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 3

ER -