# Mickelsson algebras and representations of Yangians

@article{Khoroshkin2009MickelssonAA, title={Mickelsson algebras and representations of Yangians}, author={S. M. Khoroshkin and Maxim Nazarov}, journal={Transactions of the American Mathematical Society}, year={2009}, volume={364}, pages={1293-1367} }

We use the theory of reductive dual pairs due to Howe to obtain explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra, and of the twisted Yangians corresponding to the symplectic and orthogonal Lie algebras.

## 26 Citations

### Representations of the Yangian of a Lie superalgebra of type

- Mathematics
- 2013

We describe the finite-dimensional irreducible representations of the Yangian of a Lie superalgebra of type . We formulate and prove a criterion for an irreducible representation to be…

### Twisted Yangians for symmetric pairs of types B, C, D

- Mathematics
- 2014

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan’s classification. These algebras can be regarded as coideal…

### Diagonal reduction algebra and the reflection equation

- Mathematics
- 2015

We describe the diagonal reduction algebra D(gln) of the Lie algebra gln in the R-matrix formalism. As a byproduct we present two families of central elements and the braided bialgebra structure of…

### A direct proof of a generalized harish-chandra isomorphism

- Mathematics
- 2012

A direct proof of a Harish-Chandra isomorphism recently established by Khoroshkin, Nazarov and Vinberg [10] involving Zhelobenko operators, is given. A key point is the computation of certain…

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