On Some Families of Modules for the Current Algebra

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• 作者：Matthew Bennet ; Rollo Jenkins
• 关键词：Current algebra ; Lie algebra ; Tilting module ; Symmetric group ; Graded module
• 刊名：Algebras and Representation Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：20
• 期：1
• 页码：197-208
• 全文大小：
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079
• 卷排序：20

文摘

Given a finite-dimensional module V for a finite-dimensional, complex semi-simple Lie algebra \(\mathcal {g}\), and a positive integer m, we construct a family of graded modules for the current algebra \(\mathcal {g}[t]\) indexed by simple C\(\mathcal {S}_{m}\)-modules. These modules are free of finite rank for the ring of symmetric polynomials and so can be localized to give finite-dimensional graded \(\mathcal {g}[t]\)-modules. We determine the graded characters of these modules and show that these graded characters admit a curious duality.