117 research outputs found

    Yangian of the Queer Lie Superalgebra

    Full text link
    Take the matrix Lie superalgebra glN∣Ngl_{N|N} with the standard generators EijE_{ij} where i,j=βˆ’N,...,βˆ’1,1,...,Ni,j=-N,...,-1,1,...,N. Define an involutive automorphism of glN∣Ngl_{N|N} by sending EijE_{ij} to Eβˆ’i,βˆ’jE_{-i,-j}. Then the corresponding twisted subalgebra gg in the polynomial current Lie superalgebra glN∣N[u]gl_{N|N}[u], has a natural Lie co-superalgebra structure. Here we quantise the universal enveloping algebra U(g)U(g) as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a class of irreducible representations of the quantised algebra, by introducing an appropriate analogue of the degenerate affine Hecke algebra.Comment: AmS-TeX, 28 pages, Section 2 streamline

    Yangians and Mickelsson Algebras I

    Full text link
    We study the composition of the functor 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 introduced by I. Cherednik, with the functor from the latter category to the category of modules over the Yangian Y(gl_n) due to V. Drinfeld. We propose a representation theoretic explanation of a link between the intertwining operators on the tensor products of Y(gl_n)-modules, and the `extremal cocycle' on the Weyl group of gl_m defined 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.Comment: publication details added. arXiv admin note: substantial text overlap with arXiv:math/060627
    • …
    corecore