For the affine Lie algebra A(2)2l, global Weyl modules are filtered by Demazure slices, the character of a Demazure slice is a nonsymmetric Macdonald-Koornwinder polynomial divided by its norm, and global Weyl modules for the special current algebra are free over their endomorphism ring.
Representation theoretic realization of non-symmetric Macdonald polynomials at infinity
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abstract
We study the nonsymmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the nonsymmetric Macdonald polynomials specialized at infinity. Second, we show that these modules are isomorphic to the dual spaces of sections of certain sheaves on the semi-infinite Schubert varieties. Third, we prove that the global versions of these modules are homologically dual to the level one affine Demazure modules.
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Demazure slices of type $A_{2l}^{(2)}$
For the affine Lie algebra A(2)2l, global Weyl modules are filtered by Demazure slices, the character of a Demazure slice is a nonsymmetric Macdonald-Koornwinder polynomial divided by its norm, and global Weyl modules for the special current algebra are free over their endomorphism ring.