The Clifford algebras are analogous to the Weyl algebras in the same way that the exterior algebras are analogous to the symmetric algebras.
How are the Clifford and Weyl algebras analogous? The Clifford algebras are about generators that square to $0,1,-1$ while the Weyl algebras are about differential operators with polynomial coefficients.
And how is the Weyl algebra related to the symmetric algebra?
