Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector invariants for the two dimensional modular representation of a
  cyclic group of prime order   In this paper, we study the vector invariants, ${\bf{F}}[m V_2]^{C_p}$, of
the 2-dimensional indecomposable representation $V_2$ of the cylic group,
$C_p$, of order $p$ over a field ${\bf{F}}$ of characteristic $p$. This ring of
invariants was first studied by David Richman \cite{richman} who showed that
this ring required a generator of degree $m(p-1)$, thus demonstrating that the
result of Noether in characteristic 0 (that the ring of invariants of a finite
group is always generated in degrees less than or equal to the order of the
group) does not extend to the modular case. He also conjectured that a certain
set of invariants was a generating set with a proof in the case $p=2$. This
conjecture was proved by Campbell and Hughes in \cite{campbell-hughes}. Later,
Shank and Wehlau in \cite{cmipg} determined which elements in Richman's
generating set were redundant thereby producing a minimal generating set.
  We give a new proof of the result of Campbell and Hughes, Shank and Wehlau
giving a minimal algebra generating set for the ring of invariants ${\bf{F}}[m
V_2]^{C_p}$. In fact, our proof does much more. We show that our minimal
generating set is also a SAGBI basis for ${\bf{F}}[m V_2]^{C_p}$. Further, our
techniques also serve to give an explicit decomposition of ${\bf{F}}[m V_2]$
into a direct sum of indecomposable $C_p$-modules. Finally, noting that our
representation of $C_p$ on $V_2$ is as the $p$-Sylow subgroup of $SL_2({\bf
F}_p)$, we are able to determine a generating set for the ring of invariants of
${\bf{F}}[m V_2]^{SL_2({\bf F}_p)}$.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph