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

Fei-Fei Duan; Bin Shu; Yu-Feng Yao

doi:10.4171/prims/56-4-3

JournalsprimsVol. 56, No. 4pp. 743–760

The Category $O$ 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 $W (n), S (n)$ and $H (n) (n \geq 2)$ , 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 $O$ 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