  A "flip-and-reversal" involution arising in the study of quasisymmetric Schur
functions provides a passage between what we term "Young" and "reverse"
variants of bases of polynomials or quasisymmetric functions. Building on this
perspective, which has found recent application in the study of $q$-analogues
of combinatorial Hopf algebras and generalizations of dual immaculate
functions, we develop and explore Young analogues of well-known bases for
polynomials. We prove several combinatorial formulas for the Young analogue of
the key polynomials, show that they form the generating functions for left
keys, and provide a representation-theoretic interpretation of Young key
polynomials as traces on certain modules. We also give combinatorial formulas
for the Young analogues of Schubert polynomials, including their crystal graph
structure. We moreover determine the intersections of (reverse) bases and their
Young counterparts, further clarifying their relationships to one another.
