  For any two involutions y,w in a Weyl group (y\le w), let P_{y,w} be the
polynomial defined in [KL]. In this paper we define a new polynomial
P^\sigma_{y,w} whose i-th coefficient is a_i-b_i where the i-th coefficient of
P_{y,w} is a_i+b_i (a_i,b_i are natural numbers). These new polynomials are of
interest for the theory of unitary representations of complex reductive groups.
We present an algorithm for computing these polynomials.
