  The first sections contain a survey of the application of the
Knuth-Robinson-Schensted corerspondence to the computation of Groebner bases of
determinantal ideals. We also set up a conceptual framework for this
application in terms of so-called "KRS invariants". Then we show that the
initial ideal of a determinantal ideal "defined by shape" is given by its KRS
image. We furthermore characterize those among these ideals that even have a
Groebner basis of products of minors, and show that they can be characterized
in terms of Greene's KRS invariants. Furthermore it is shown that for the ideal
generated by all t-minors the formation of initial ideal and symbolic power
commutes. The last section contains a discussion of potential KRS invariants
related to so-called 1-cogenerated ideals.
