On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

Fei Fei Duan; Bin Shu; Yu Feng Yao

doi:10.1007/s10114-020-9469-z

On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

Fei Fei Duan^*
, Bin Shu
, Yu Feng Yao

^*Corresponding author for this work

School of Mathematical Sciences

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

1 Scopus citations

Abstract

Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac’s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.

Original language	English
Pages (from-to)	1061-1075
Number of pages	15
Journal	Acta Mathematica Sinica, English Series
Volume	36
Issue number	9
DOIs	https://doi.org/10.1007/s10114-020-9469-z
State	Published - 1 Sep 2020

Keywords

17B10
17B66
17B70
Lie superalgebra of Cartan type
block
restricted representation

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title = "On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type",

abstract = "Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac{\textquoteright}s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.",

keywords = "17B10, 17B66, 17B70, Lie superalgebra of Cartan type, block, restricted representation",

author = "Duan, \{Fei Fei\} and Bin Shu and Yao, \{Yu Feng\}",

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doi = "10.1007/s10114-020-9469-z",

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AU - Duan, Fei Fei

AU - Shu, Bin

AU - Yao, Yu Feng

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac’s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.

AB - Let g be a restricted Lie superalgebra of Cartan type W(n), S(n)or H(n) over an algebraically closed field k of prime characteristic p > 3, in the sense of modular version of Kac’s definition in 1977. In this note, we show that the restricted representation category over g has only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.

KW - 17B10

KW - 17B66

KW - 17B70

KW - Lie superalgebra of Cartan type

KW - block

KW - restricted representation

UR - https://www.scopus.com/pages/publications/85090268439

U2 - 10.1007/s10114-020-9469-z

DO - 10.1007/s10114-020-9469-z

M3 - 文章

AN - SCOPUS:85090268439

SN - 1439-8516

VL - 36

SP - 1061

EP - 1075

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 9

ER -

On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

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Keywords

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