  The center of an extended affine Hecke algebra is known to be isomorphic to
the ring of symmetric functions associated to the underlying finite Weyl group
$W\_0$. The set of Weyl characters ${\sf s}\_\la$ forms a basis of the center
and Lusztig showed in [Lus15] that these characters act as translations on the
Kazhdan-Lusztig basis element $C\_{w\_0}$ where $w\_0$ is the longest element
of $W\_0$, that is we have $C\_{w\_0}{\sf s}\_\la =C\_{w\_0t\_\la}$. As a
consequence, the coefficients that appear when
decomposing~$C\_{w\_0t\_{\la}}{\sf s}\_\tau$ in the Kazhdan-Lusztig basis are
tensor multiplicities of the Lie algebra with Weyl group $W\_0$. The aim of
this paper is to explain how admissible subsets and Littelmann paths, which are
models to compute such multiplicities, naturally appear when working out this
decomposition.
