Realizations of
نویسندگان
چکیده
In this paper, we give an explicit realization of all irreducible modules in Chari’s category O ~ \widetilde {\mathcal O} for the affine Kac-Moody algebra alttext="upper A 1 Superscript left-parenthesis right-parenthesis"> A 1 ( stretchy="false">) encoding="application/x-tex">A_{1}^{(1)} by using idea free fields. We work on a much more general setting which also gives us realizations simple weight certain current alttext="German s German l Subscript 2 Baseline double-struck C mathvariant="fraktur">s mathvariant="fraktur">l 2 mathvariant="double-struck">C encoding="application/x-tex">\mathfrak {sl}_2(\mathbb {C}) with finite multiplicities, including polynomial right-parenthesis circled-times left-bracket t right-bracket"> ⊗<!-- ⊗ stretchy="false">[ t stretchy="false">] {C})\otimes \mathbb {C}[t] , loop comma negative , −<!-- − </mml:msup> {C}[t,t^{-1}] and three-point Lie minus {C}[t,t^{-1},(t-1)^{-1}] arisen Kazhdan-Lusztig.
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ژورنال
عنوان ژورنال: Representation Theory of The American Mathematical Society
سال: 2023
ISSN: ['1088-4165']
DOI: https://doi.org/10.1090/ert/632