The category 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

The category O for lie algebras of vector fields (I): Tilting modules and character formulas

Fei Fei Duan
, Bin Shu
, Yu Feng Yao

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 ≥ 2), and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

Original language	English
Pages (from-to)	743-760
Number of pages	18
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	56
Issue number	4
DOIs	https://doi.org/10.4171/PRIMS/56-4-3
State	Published - 2020

Keywords

Character formulas
Lie algebras of vector fields
Tilting modules

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10.4171/PRIMS/56-4-3

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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 ≥ 2), and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.",

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AU - Duan, Fei Fei

AU - Shu, Bin

AU - Yao, Yu Feng

PY - 2020

Y1 - 2020

N2 - 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 ≥ 2), and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

AB - 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 ≥ 2), and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

KW - Character formulas

KW - Lie algebras of vector fields

KW - Tilting modules

UR - https://www.scopus.com/pages/publications/85092413466

U2 - 10.4171/PRIMS/56-4-3

DO - 10.4171/PRIMS/56-4-3

M3 - 文章

AN - SCOPUS:85092413466

SN - 0034-5318

VL - 56

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EP - 760

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 4

ER -

The category O for lie algebras of vector fields (I): Tilting modules and character formulas

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