The ring Rm of m-symmetric functions consists of the formal power series that are symmetric in the variables xm+1,xm+2,…
Nearby in the stack
but carry no symmetry in the first
m
variables. We develop a combinatorial theory for the specialization at
t=0
of the Schur functions of
Rm
. Our main tool is a new characterization of right key tableaux as suprema of the sets of decreasing subwords of the reading words of the subtableaux of
T
. Being invariant under elementary Knuth transformations, this characterization is compatible with the RSK correspondence. We obtain in this way a generating function over semistandard tableaux for the
m
-symmetric Schur functions at
t=0
, together with a combinatorial proof of a Cauchy identity in
Rm
. The
m
-symmetric Schur functions and their dual are then respectively identified with Demazure atoms and Demazure characters. Restricted to the last
m
variables, our correspondence specializes to a proof, by ordinary RSK, of Lascoux's nonsymmetric Cauchy identity for Demazure characters and atoms. As further applications, we relate the
m
-symmetric Schur functions at
t=0
to the almost symmetric Schur functions through a unitriangular change-of-basis matrix, obtain tableau generating functions and Cauchy identities for both families, and derive Jacobi-Trudi type determinantal formulas for three different bases.