  We announce a systematic way for constructing bispectral algebras of
commuting differential operators of any rank N. It enables us to obtain all
previously known classes and examples of bispectral operators. Moreover, we
give a representation-theoretic explanation of the results including those of
Duistermaat and Gr\"unbaum. The manifold of bispectral operators of any order
is preserved by an hierarchy of symmetries. We point out that our methods
provide a completely algorithmic procedure for obtaining bispectral algebras.
We conjecture that the class built in the present paper exhausts all bispectral
scalar operators.
  The proofs and details appeared in our preprints hep-th/9510211,
q-alg/9602010, q-alg/9602011, q-alg/9602012.
