Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor factorization and Spin construction for Kac-Moody algebras   In this paper we discuss the "Factorization phenomenon" which occurs when a
representation of a Lie algebra is restricted to a subalgebra, and the result
factors into a tensor product of smaller representations of the subalgebra. We
analyze this phenomenon for symmetrizable Kac-Moody algebras (including
finite-dimensional, semi-simple Lie algebras). We present a few factorization
results for a general embedding of a symmetrizable Kac-Moody algebra into
another and provide an algebraic explanation for such a phenomenon using Spin
construction. We also give some application of these results for semi-simple
finite dimensional Lie algebras.
  We extend the notion of Spin functor from finite-dimensional to symmetrizable
Kac-Moody algebras, which requires a very delicate treatment. We introduce a
certain category of orthogonal $\g$-representations for which, surprisingly,
the Spin functor gives a $\g$-representation in Bernstein-Gelfand-Gelfand
category $\O$. Also, for an integrable representation $\Spin$ produces an
integrable representation. We give the formula for the character of Spin
representation for the above category and work out the factorization results
for an embedding of a finite dimensional semi-simple Lie algebra into its
untwisted affine Lie algebra. Finally, we discuss classification of those
representations for which $\Spin$ is irreducible.

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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc