Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Modular Invariants of A Vector and A Covector   Let $SL_{2}(F_{q})$ be the special linear group over a finite field $F_{q}$,
$V$ be the 2-dimensional natural representation of $SL_{2}(F_{q})$ and
$V^{\ast}$ be the dual representation. We denote by $F_{q}[V\oplus
V^{\ast}]^{SL_{2}(F_{q})}$ the corresponding invariant ring of a vector and a
covector for $SL_{2}(F_{q})$. In this paper, we construct a free module basis
over some homogeneous system of parameters of $F_{q}[V\oplus
V^{\ast}]^{SL_{2}(F_{q})}$. We calculate the Hilbert series of $F_{q}[V\oplus
V^{\ast}]^{SL_{2}(F_{q})}$, and prove that it is a Gorenstein algebra. As an
application, we confirm a special case of the recent conjecture of Bonnafe and
Kemper in 2011.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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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: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg