Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a generalization of Dipper--James--Murphy's Conjecture   Let $K$ be a field and $q\in K^{\times}$. Let $e$ be the multiplicative order
of $q$; or 0 if $q$ is not a root of unity. Let $\bQ:=(q^{v_1},...,q^{v_r})$.
Let ${K}_r(n)$ be the set of Kleshchev $r$-multipartitions with respect to
$(e;\bQ)$. In this paper, we consider an extention of Dipper--James--Murphy's
Conjecture to the Ariki--Koike algebra $H_{r,n}(q;\bQ)$ with $r>2$. We show
that any $(\bQ,e)$-restricted $r$-multipartition of $n$ is a Kleshchev
multipartition in ${K}_r(n)$; and if $e>1$, then any multi-core
$\ulam=(\lam^{(1)},...,\lam^{(r)})$ in ${K}_r(n)$ is a $(\bQ,e)$-restricted
$r$-multipartition. As a consequence, we show that if $e=0$ (i.e., $q$ is not a
root of unity), then ${K}_r(n)$ coincides with the set of $(\bQ,e)$-restricted
$r$-multipartitions of $n$ and also coincides with the set of ladder
$r$-multipartitions of $n$.

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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-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: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph