By letting *q*=0, we obtain *t*-deformations of key polynomials and Demazure atoms and
we show that the Hall-Littlewood polynomials expand positively into these deformations.
This generalizes a result by Haglund, Luoto, Mason and van Willigenburg.
As a corollary, the Schur polynomials decompose with non-negative coefficients
into *t*-deformations of general Demazure atoms and
thus generalize the *t*=0 case which was previously known.
This gives a unified formula for the classical expansion
of Schur polynomials in Hall-Littlewood polynomials
and the expansion of Schur polynomials into Demazure atoms.

Received: April 15, 2016. Accepted: May 30, 2019. Final Version: July 30, 2019.

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