Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kostka multiplicity one for multipartitions   If $[\lambda(j)]$ is a multipartition of the positive integer $n$ (a sequence
of partitions with total size $n$), and $\mu$ is a partition of $n$, we study
the number $K_{[\lambda(j)]\mu}$ of sequences of semistandard Young tableaux of
shape $[\lambda(j)]$ and total weight $\mu$. We show that the numbers
$K_{[\lambda(j)] \mu}$ occur naturally as the multiplicities in certain
permutation representations of wreath products. The main result is a set of
conditions on $[\lambda(j)]$ and $\mu$ which are equivalent to $K_{[\lambda(j)]
\mu} = 1$, generalizing a theorem of Berenshte\u{\i}n and Zelevinski\u{\i}. We
also show that the questions of whether $K_{[\lambda(j)] \mu} > 0$ or
$K_{[\lambda(j)] \mu} = 1$ can be answered in polynomial time, expanding on a
result of Narayanan. Finally, we give an application to multiplicities in the
degenerate Gel'fand-Graev representations of the finite general linear group,
and we show that the problem of determining whether a given irreducible
representation of the finite general linear group appears with nonzero
multiplicity in a given degenerate Gel'fand-Graev representation, with their
partition parameters as input, is $NP$-complete.

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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: eess