Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Steinberg type decomposition theorem for higher level Demazure modules   We study Demazure modules which occur in a level $\ell$ irreducible
integrable representation of an affine Lie algebra. We also assume that they
are stable under the action of the standard maximal parabolic subalgebra of the
affine Lie algebra. We prove that such a module is isomorphic to the fusion
product of "prime" \ Demazure modules, where the prime factors are indexed by
dominant integral weights which are either a multiple of $\ell$ or take value
less than $\ell$ on all simple coroots. Our proof depends on a technical result
which we prove in all the classical cases and $G_2$. Calculations with
mathematica show that this result is correct for small values of the level.
Using our result, we show that there exist generalizations of $Q$--systems to
pairs of weights where one of the weights is not necessarily rectangular and is
of a different level. Our results also allow us to compare the multiplicities
of an irreducible representation occuring in the tensor product of certian
pairs of irreducible representations, i.e., we establish a version of Schur
positvity for such pairs of irreducible modules for a simple Lie algebra.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: physics