Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit expressions for \vSapovalov elements in Type A   We give explicit expressions for \vSapovalov elements in Type A Lie algebras
and superalgebras. Explicit expressions were already given in arXiv:1710.10528
Section 9, using non-commutative determinants, and in fact our first main
results, Theorems 2.3 and 2.6 can be viewed as complete expansions of these
determinants. But we give new proofs, which seem easier because they avoid
induction and cofactor expansion. We also describe \vSapovalov elements for
fgl(m,n)with respect to an arbitrary Borel subalgebra in Theorem 3.7, and
interpret \vSapovalov elements in Type A as determinants of Hessenberg matrices
in Theorems 4.5 and 4.9.The exact form of the explicit expressions depends on
an ordering on the set of positive roots, and Hessenberg matrices are useful in
changing the ordering. Having explicit expressions for \vSapovalov elements
allows us to give easy proofs of several results in representation theory, see
Section 6 and Subsection 4.6.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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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: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-ex