  Take the degenerate affine Hecke algebra $H_{l+m}$ corresponding to the group
$GL_{l+m}$ over a $p$-adic field. 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 complex numbers $z$ and $w$. There is a canonical operator $J$
acting in $W$, it corresponds to the rational Yang $R$-matrix.
  The algebra $H_{l+m}$ contains the symmetric group $S_{l+m}$, and $J$
commutes with the action of $S_{l+m}$ in $W$. 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 obtain a nice formula for the
ratio of two eigenvalues of $J$, corresponding to the "highest" and "lowest"
(multiplicity-free) irreducible components of $W$.
