A mixture of the tensor algebra and the infinite symmetric group and its application to the Schur--Weyl duality

We introduce a new algebra, which can be regarded as a mixture of the
tensor algebra and the infinite symmetric group.  As basic operators  on
this algebra, we can consider "multiplications" by vectors and
"derivations" by convectors.  These two types of operators satisfy an
analogue of the canonical commutation relations, and we can regard the
operator algebra generated by these as an analogue of the Weyl algebra  and
the Clifford algebra.  These algebras have applications to  noncommutative
invariant theory (for example, a simple proof of the  Schur--Weyl duality,
and invariant theory in the tensor algebra and  the universal enveloping
algebra of the general linear Lie algebra).

A q-analogue version of this result is also in progress.  However I  would
like to explain the basic idea in the classical setting.