We present J, H and K-band spectroscopy of Cygnus A, spanning 1.0-2.4 mum i
n the rest-frame and hence several rovibrational H-2, H recombination and [
Fe II] emission lines. The lines are spatially extended by up to 6 kpc from
the nucleus, but their distinct kinematics indicate that the three groups
(H, H-2 and [Fe II]) are not wholly produced in the same gas. The broadest
line, [Fe II]lambda1.644, exhibits a non-Gaussian profile with a broad base
(FWHM similar or equal to 1040 km s(-1)), perhaps because of the interacti
on with the radio source. Extinctions to the line-emitting regions substant
ially exceed earlier measurements based on optical H recombination lines.
Hard X-rays from the quasar nucleus are likely to dominate the excitation o
f the H-2 emission. The results of Maloney, Hollenbach & Tielens are thus u
sed to infer the total mass of gas in H-2 v=1-0 S(1)-emitting clouds as a f
unction of radius, for gas densities of 10(3) and 10(5) cm(-3), and stoppin
g column densities N-H=10(22)-10(24) cm(-2). Assuming azimuthal symmetry, a
t least 2.3x10(8) M-. of such material is present within 5 kpc of the nucle
us, if the line-emitting clouds see an unobscured quasar spectrum. Alternat
ively, if the bulk of the X-ray absorption to the nucleus inferred by Ueno
et al. actually arises in a circumnuclear torus, the implied gas mass rises
to similar to 10(10) M-.. The latter plausibly accounts for 10(9) yr of ma
ss deposition from the cluster cooling flow, for which (M) over dot similar
or equal to 10M(.)yr(-1) within this radius.