Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mixed hook-length formula for affine Hecke algebras   Consider the affine Hecke algebra $H_l$ corresponding to the group $GL_l$
over a $p$-adic field with the residue field of cardinality $q$. Regard $H_l$
as an associative algebra over the field $C(q)$. Consider the $H_{l+m}$-module
$W$ induced from the tensor product of the evaluation modules over the algebras
$H_l$ and $H_m$. The module $W$ depends on two partitions $\lambda$ of $l$ and
$\mu$ of $m$, and on two non-zero elements of the field $C(q)$. There is a
canonical operator $J$ acting on $W$, it corresponds to the trigonometric
$R$-matrix. The algebra $H_{l+m}$ contains the finite dimensional Hecke algebra
of rank $l+m$ as a subalgebra, and the operator $J$ commutes with the action of
this subalgebra on $W$. Under this action, $W$ decomposes into irreducible
subspaces according to the Littlewood-Richardson rule. We compute the
eigenvalues of $J$, corresponding to certain multiplicity-free irreducible
components of $W$. In particular, we give a formula for the ratio of two
eigenvalues of $J$, corresponding to the ``highest'' and the ``lowest''
components. As an application, we derive the well known $q$-analogue of the
hook-length formula for the number of standard tableaux of shape $\lambda$.

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The categories of this paper are: bayes-an
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg