We consider a Demazure slice of type \(A_{2l}^{(2)}\), that is an associated graded piece of an infinite-dimensional version of a Demazure module. We show that a global Weyl module of a hyperspecial current algebra of type \(A_{2l}^{(2)}\) is filtered by Demazure slices. We calculate extensions between a Demazure slice and a usual Demazure module and prove that a graded character of a Demazure slice is equal to a nonsymmetric Macdonald-Koornwinder polynomial divided by its square norm. In the last section, we prove that a global Weyl module of the special current algebra of type \(A_{2l}^{(2)}\) is a free module over the polynomial ring arising as the endomorphism ring of itself.

我们考虑类型为\（A_ {2l} ^ {（2）} \）的Demazure切片，它是Demazure模块的无穷大版本的关联的渐变片。我们显示了Demazure切片对类型为\（A_ {2l} ^ {（2）} \）的超特殊当前代数的全局Weyl模块进行了过滤。我们计算了Demazure切片和常规Demazure模块之间的扩展，并证明了Demazure切片的渐变字符等于非对称Macdonald-Koornwinder多项式除以其平方范数。在最后一节中，我们证明类型为\（A_ {2l} ^ {（2）} \）的特殊当前代数的全局Weyl模块是作为自身的内同态环而出现的多项式环上的自由模块。