In the recently proposed generalization of the Yang-Mills theory the group of
gauge transformation gets essentially enlarged. This enlargement involves an
elegant mixture of the internal and space-time symmetries. The resulting group
is an extension of the Poincar\'e group with infinitely many generators which
carry internal and space-time indices. This is similar to the super-symmetric
extension of the Poincar\'e group, where instead of an anti-commuting spinor
variable one should introduce a new vector variable. The construction of
irreducible representations of the extended Poincar\'e algebra identifies a
vector variable with the derivative of the Pauli-Lubanski vector over its
length. As a result of this identification the generators of the gauge group
have nonzero components only in the plane transversal to the momentum and are
projecting out non-Abelian tensor gauge fields into the transversal plane,
keeping only their positively definite space-like components.Comment: 21 page