We give a new and independent parametrization of the
set of discrete series characters of an affine Hecke algebra
, in terms of a
canonically defined basis
of a certain lattice of virtual elliptic characters of the underlying (extended) affine
Weyl group. This classification applies to all semisimple affine Hecke algebras
, and
to all
,
where
denotes the vector group of positive real (possibly unequal) Hecke parameters for
. By analytic Dirac
induction we define for each
a continuous (in the sense of Opdam and Solleveld (2010)) family
, such that
(for some
) is an irreducible discrete
series character of
.
Here
is a finite union
of hyperplanes in
.
In the nonsimply laced cases we show that the families of virtual discrete series characters
are piecewise rational in the
parameters
. Remarkably,
the formal degree of
in such piecewise rational family turns out to be rational. This implies that for each
there exists a universal
rational constant
determining the formal degree in the family of discrete series characters
. We will compute the
canonical constants
,
and the signs
.
For certain geometric parameters we will provide the comparison with the
Kazhdan–Lusztig–Langlands classification.