  In this note we determine the values of parameters c for which the polynomial
representation of the degenerate double affine Hecke algebra (DAHA), i.e. the
trigonometric Cherednik algebra, is reducible. Namely, we show that c is a
reducibility point for the polynomial representation of the trigonometric
Cherednik algebra for a root system R if and only if it is a reducibility point
for the rational Cherednik algebra for the Weyl group of some root subsystem R'
of R of the same rank; such subsystems for any R are given by the well known
Borel-de Siebenthal algorithm. This result has been proved by Cherednik using a
case-by-case method.
