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We show that combinatorial objects called row-strict composition tableaux,introduced by Mason and Remmel in 2014 and closely related to thequasi-symmetric Schur functions of Haglund-Luoto-Mason-van Willigenburg, form abasis for Schur functors of finite free modules over arbitrary commutativerings. When the ring is the complex numbers, this produces a new basis for theirreducible polynomial representations of $\operatorname{GL}_n(\mathbb{C})$.Moreover, in this case it also produces new basis for the Pl\"ucker algebra, asubalgebra of the polynomial ring over $\mathbb{C}$ in $n^2$ variables, whichis of independent combinatorial and geometric interests. As an aside we alsoshow that these results hold for other combinatorial objects called reverse rowstrict tableau.

Composition Tableaux basis for Schur functors and the Pl\"ucker algebra