Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bigrassmannian permutations and Verma modules   We show that bigrassmannian permutations determine the socle of the cokernel
of an inclusion of Verma modules in type $A$. All such socular constituents
turn out to be indexed by Weyl group elements from the penultimate two-sided
cell. Combinatorially, the socular constituents in the cokernel of the
inclusion of a Verma module indexed by $w\in S_n$ into the dominant Verma
module are shown to be determined by the essential set of $w$ and their degrees
in the graded picture are shown to be computable in terms of the associated
rank function. As an application, we compute the first extension from a simple
module to a Verma module.

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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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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: q-alg
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc