Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A basis for the full Homfly skein of the annulus   The meridian maps of the full Homfly skein of the annulus are linear
endomorphisms induced by the insertion of a meridian loop, with either
orientation, around a diagram in the annulus. The eigenvalues of the meridian
maps are known to be distinct, and are indexed by pairs of partitions of
integers p and n into k and k* parts respectively.
  We give here an explicit formula for a corresponding eigenvector as the
determinant of a (k*+k)x(k*+k) matrix whose entries are skein elements
corresponding to partitions with a single part. This extends the results of
Kawagoe and Lukac, for the case p=0, giving a basis for the subspace of the
skein spanned by closed braids all oriented in the same direction. Their
formula uses the Jacobi-Trudy determinants for Schur functions in terms of
complete symmetric functions. Our matrices have a similar pattern of entries in
k rows, and a modified pattern in k* rows, resulting in a combination of closed
braids with up to n strings oriented in one direction and p in the reverse
direction.
  We discuss the 2-variable knot invariants resulting from decoration of a knot
by these skein elements, and their relation to unitary quantum invariants.

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The categories of this paper are: econ
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol