The Category for Lie Algebras of Vector Fields (I): Tilting Modules and Character Formulas

  • Fei-Fei Duan

    Hebei Normal University, Shijiazhuang, Hebei, China
  • Bin Shu

    East China Normal University, Shanghai, China
  • Yu-Feng Yao

    Shanghai Maritime University, China
The Category $\mathcal O$ for Lie Algebras of Vector Fields (I): Tilting Modules and Character Formulas cover

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Abstract

In this article, we exploit the theory of graded module categories with semi-infinite character developed by Soergel (Character formulas for tilting modules over Kac–Moody algebras, Represent. Theor. 2 (1998), 432–448) to study representations of infinite-dimensional Lie algebras of vector fields and , and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

Cite this article

Fei-Fei Duan, Bin Shu, Yu-Feng Yao, The Category for Lie Algebras of Vector Fields (I): Tilting Modules and Character Formulas. Publ. Res. Inst. Math. Sci. 56 (2020), no. 4, pp. 743–760

DOI 10.4171/PRIMS/56-4-3