Abstract
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.
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The author thanks Syu Kato and Ievgen Makedonskyi for much advice and discussion.
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Presented by: Vyjayanthi Chari
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Chihara, M. Demazure Slices of Type \(A_{2l}^{(2)}\). Algebr Represent Theor 25, 491–519 (2022). https://doi.org/10.1007/s10468-021-10032-2
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DOI: https://doi.org/10.1007/s10468-021-10032-2