  Non-attacking skyline fillings were used by Haglund, Haiman and Loehr to
establish a combinatorial formula for nonsymmetric Macdonald polynomials.
Semistandard skyline fillings are non-attacking skyline fillings with both
major index and coinversion number equal to zero, which serve as a
combinatorial model for key polynomials. In this paper, we construct an
involution on semistandard skyline fillings. This involution can be viewed as a
vast generalization of the classical Bender--Knuth involution. As an
application, we obtain that semistandard skyline fillings are compatible with
the Demazure operators, offering a new combinatorial proof that nonsymmetric
Macdonald polynomials specialize to key polynomials.
