Abstract
We prove that the complement to the affine complex arrangement of type
\widetilde B_n
is a
K(π,1)
space. We also compute the cohomology of the affine Artin group
G_{\widetilde B_n}
(of type
\widetilde B_n
) with coefficients in interesting local systems. In particular, we consider the module
ℚ[q^{±1} ,t^{±1}]
, where the first
n
standard generators of
G_{\widetilde B_n}
act by
(−q)
-multiplication while the last generator acts by
(−t)
multiplication. Such a representation generalizes the analogous 1-parameter representation related to the bundle structure over the complement to the discriminant hypersurface, endowed with the monodromy action of the associated Milnor fibre. The cohomology of
G_{\widetilde B_n}
with trivial coefficients is derived from the previous one.