Blocks and characters of G(3)-modules of non-integral weights

Chih Whi Chen; Shun Jen Cheng; Li Luo

doi:10.1016/j.jalgebra.2021.09.006

Blocks and characters of G(3)-modules of non-integral weights

Chih Whi Chen^*
, Shun Jen Cheng
, Li Luo

^*Corresponding author for this work

School of Mathematical Sciences

Department of Mathematics
National Central University
Academia Sinica - Institute of Mathematics

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

1 Scopus citations

Abstract

We classify blocks in the BGG category O of modules of non-integral weights for the exceptional Lie superalgebra G(3). We compute the characters for tilting modules of non-integral weights in O. Reduction methods are established to connect non-integral blocks of G(3) with blocks of the special linear Lie algebra sl(2), the exceptional Lie algebra G₂, the general linear Lie superalgebras gl(1|1), gl(2|1) and the ortho-symplectic Lie superalgebra osp(3|2).

Original language	English
Pages (from-to)	574-616
Number of pages	43
Journal	Journal of Algebra
Volume	588
DOIs	https://doi.org/10.1016/j.jalgebra.2021.09.006
State	Published - 15 Dec 2021

Keywords

Bernstein-Gelfand-Gelfand categories O
Blocks
Characters
Exceptional Lie superalgebras
Lie algebras
Lie superalgebras
Tilting modules

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10.1016/j.jalgebra.2021.09.006

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title = "Blocks and characters of G(3)-modules of non-integral weights",

abstract = "We classify blocks in the BGG category O of modules of non-integral weights for the exceptional Lie superalgebra G(3). We compute the characters for tilting modules of non-integral weights in O. Reduction methods are established to connect non-integral blocks of G(3) with blocks of the special linear Lie algebra sl(2), the exceptional Lie algebra G2, the general linear Lie superalgebras gl(1|1), gl(2|1) and the ortho-symplectic Lie superalgebra osp(3|2).",

keywords = "Bernstein-Gelfand-Gelfand categories O, Blocks, Characters, Exceptional Lie superalgebras, Lie algebras, Lie superalgebras, Tilting modules",

author = "Chen, \{Chih Whi\} and Cheng, \{Shun Jen\} and Li Luo",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

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day = "15",

doi = "10.1016/j.jalgebra.2021.09.006",

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T1 - Blocks and characters of G(3)-modules of non-integral weights

AU - Chen, Chih Whi

AU - Cheng, Shun Jen

AU - Luo, Li

PY - 2021/12/15

Y1 - 2021/12/15

N2 - We classify blocks in the BGG category O of modules of non-integral weights for the exceptional Lie superalgebra G(3). We compute the characters for tilting modules of non-integral weights in O. Reduction methods are established to connect non-integral blocks of G(3) with blocks of the special linear Lie algebra sl(2), the exceptional Lie algebra G2, the general linear Lie superalgebras gl(1|1), gl(2|1) and the ortho-symplectic Lie superalgebra osp(3|2).

AB - We classify blocks in the BGG category O of modules of non-integral weights for the exceptional Lie superalgebra G(3). We compute the characters for tilting modules of non-integral weights in O. Reduction methods are established to connect non-integral blocks of G(3) with blocks of the special linear Lie algebra sl(2), the exceptional Lie algebra G2, the general linear Lie superalgebras gl(1|1), gl(2|1) and the ortho-symplectic Lie superalgebra osp(3|2).

KW - Bernstein-Gelfand-Gelfand categories O

KW - Blocks

KW - Characters

KW - Exceptional Lie superalgebras

KW - Lie algebras

KW - Lie superalgebras

KW - Tilting modules

UR - https://www.scopus.com/pages/publications/85115365548

U2 - 10.1016/j.jalgebra.2021.09.006

DO - 10.1016/j.jalgebra.2021.09.006

M3 - 文章

AN - SCOPUS:85115365548

SN - 0021-8693

VL - 588

SP - 574

EP - 616

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Blocks and characters of G(3)-modules of non-integral weights

Abstract

Keywords

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