Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propri\'et\'es de maximalit\'e concernant une repr\'esentation d\'efinie
  par Lusztig   Let $\lambda$ be a symplectic partition, denote Jord^{bp}($\lambda$) the set
of even positive integers i which appear in $\lambda$, and let a map
$\epsilon:Jord^{bp}(\lambda) \to {\pm 1}$. The generalized Springer's
correspondence associates to $(\lambda,\epsilon)$ an irreducible representation
$\rho(\lambda,\epsilon)$ of some Weyl group. We can also define a
representation $\underline{\rho}(\lambda,\epsilon)$ of the same Weyl group, in
general reducible. Roughly speaking, $\rho(\lambda,\epsilon)$ is the
representation of the Weyl group in the top cohomology group of some variety
and $\underline{\rho}$ is the representation in the sum of all the cohomology
groups of the same variety. The representation $\underline{\rho}$ decomposes as
a direct sum of $\rho(\lambda',\epsilon')$ with some multiplicities, where
$(\lambda',\epsilon')$ describes the pairs similar to $(\lambda,\epsilon)$. It
is well know that $(\lambda,\epsilon)$ appears in this decomposition with
multiplicity one and is minimal in this decomposition. That is, if
$(\lambda',\epsilon')$ appears, we have $\lambda'>\lambda$ or
$(\lambda',\epsilon')=(\lambda,\epsilon)$. Assuming that $\lambda$ has only
even parts, we prove that there exists also a maximal pair
$(\lambda^{max},\epsilon^{max})$. That is $4(\lambda^{max},\epsilon^{max})$
appears with positive multiplicity (in fact one) and, if $(\lambda',\epsilon')$
appears, we have $\lambda^{max}>\lambda'$ or
$(\lambda',\epsilon')=(\lambda^{max},\epsilon^{max})$.

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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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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: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas