Abstract
Let
U
be the quantum group with divided powers in
p−
th root of unity for prime
p
. For any two-sided cell
A
in the corresponding affine Weyl group one associates tensor ideal in the category of tilting modules over
U
. In this note we show that for any cell
A
there exists tilting module
T
from the corresponding tensor ideal such that biggest power of
p
which divides
dimT
is
p
a(A)
where
a(A)
is Lusztig's
a−
function. In new version some typos are corrected and exposition is improved following suggestions of the referee.