119 research outputs found
Yangian of the Queer Lie Superalgebra
Take the matrix Lie superalgebra with the standard generators
where . Define an involutive automorphism of
by sending to . Then the corresponding twisted
subalgebra in the polynomial current Lie superalgebra , has a
natural Lie co-superalgebra structure. Here we quantise the universal
enveloping algebra 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
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
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