Macdonald polynomials and level two Demazure modules for affine <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">sl</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>

We define a family of symmetric polynomials Gν,λ(z1,…,zn+1,q) indexed by pair dominant integral weights for root system type An. The polynomial Gν,0(z,q) is the specialized Macdonald Pν(z,q,0) and known to be graded character level one Demazure module associated affine Lie algebra slˆn+1. prove that G0,λ(z,q) two Under suitable conditions on (ν,λ) (which apply pairs (ν,0) (0,λ)) we Gν,λ(z,q) Schur positive, i.e., it can written as linear combination with coefficients in Z+[q]. further elements being essentially products q-binomials. Together result K. Naoi, consequence our an explicit formula non-simply laced characters algebra.