1,156 research outputs found
On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12
We consider additive codes over GF(4) that are self-dual with respect to the
Hermitian trace inner product. Such codes have a well-known interpretation as
quantum codes and correspond to isotropic systems. It has also been shown that
these codes can be represented as graphs, and that two codes are equivalent if
and only if the corresponding graphs are equivalent with respect to local
complementation and graph isomorphism. We use these facts to classify all codes
of length up to 12, where previously only all codes of length up to 9 were
known. We also classify all extremal Type II codes of length 14. Finally, we
find that the smallest Type I and Type II codes with trivial automorphism group
have length 9 and 12, respectively.Comment: 18 pages, 4 figure
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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