Хорошкин Сергей Михайлович

Mickelsson algebras and representations of yangians

2012 · ARTICLE · en

Let Y(gln) be the Yangian of the general linear Lie algebra gln. We denote by Y(spn) and Y(son) the twisted Yangians corresponding to the symplectic and orthogonal subalgebras in the Lie algebra gln. These twisted Yangians are one-sided coideal subalgebras in the Hopf algebra Y(gln). We provide realizations of irreducible modules of the algebras Y(spn) and Y(son) as certain quotients of tensor products of symmetic and exterior powers of the vector space Cn. For the Yangian Y(gln) such realizations have been known, but we give new proofs of these results. For the twisted Yangian Y(spn), we realize all irreducible finite-dimensional modules. For the twisted Yangian Y(son), we realize all those irreducible finite-dimensional modules, where the action of the Lie algebra son integrates to an action of the special orthogonal Lie group SOn. Our results are based on the theory of reductive dual pairs due to Howe, and on the representation theory of Mickelsson algebras.

Structure constants of diagonal reduction algebras of gl type

2011 · ARTICLE · en

We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra gl n into gl n ⊕gl n . Its representation theory is related to the theory of decompositions of tensor products of gl n -modules.

Zero divisors in reduction algebras

2011 · PREPRINT · en

We establish the absence of zero divisors in the reduction algebra of a Lie algebra g with respect to its reductive Lie sub-algebra k. The class of reduction algebras include the Lie algebras (they arise when k is trivial) and the Gelfand–Kirillov conjecture extends naturally to the reduction algebras. We formulate the conjecture for the diagonal reduction algebras of sl type and verify it on a simplest example.

A generalized Harish-Chandra isomorphism

2011 · ARTICLE · en

Irreducible representations of Yangians

2011 · ARTICLE · en

We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion procedure for twisted Yangians. For the non-twisted Yangian, this procedure goes back to the works of Cherednik.

The weight function for the quantum affine algebra Uq(A_2^(2))

2010 · ARTICLE · en

In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra Uq(A(2)2 ). The calculations use the technique of projecting products of Drinfeld currents onto the intersection of Borel subalgebras of different types.

Erratum to: Twisted Yangians and Mickelsson algebras. I

2009 · ARTICLE · en

Bethe ansatz for the universal weight function

2009 · ARTICLE · en

We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra Uq(glN). We investigate ordering properties of the product of the transfer matrix and these vectors. We derive that these vectors are eigenvectors of the transfer matrix if their Bethe parameters satisfy the universal Bethe equations.

Скрученные янгианы и алгебры Микельссона II.

2009 · ARTICLE · ru

A computation of universal weight function for quantum affine algebra Uq(gl_N)

2008 · ARTICLE · en