A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras

Yi Yang Li; Bin Shu; Yu Feng Yao

doi:10.1016/j.jalgebra.2020.07.009

A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras

Yi Yang Li, Bin Shu, Yu Feng Yao

School of Mathematical Sciences

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

Abstract

Let G be a connected, reductive algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G). In this paper, we study representations of g with a p-character χ of standard Levi form. When g is of type A_n,B_n,C_n or D_n, a sufficient condition for the irreducibility of standard parabolic baby Verma g-modules is obtained. This partially answers a question raised by Friedlander and Parshall (1990) in [2]. Moreover, as an application, in the special case that g is of type A_n or B_n, and χ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen (1999) in [6].

Original language	English
Pages (from-to)	111-147
Number of pages	37
Journal	Journal of Algebra
Volume	563
DOIs	https://doi.org/10.1016/j.jalgebra.2020.07.009
State	Published - 1 Dec 2020

Keywords

Maximal weight vector
Nilpotent orbit
Parabolic baby Verma module
Standard Levi form
Sub-regular nilpotent orbit

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10.1016/j.jalgebra.2020.07.009

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title = "A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras",

abstract = "Let G be a connected, reductive algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G). In this paper, we study representations of g with a p-character χ of standard Levi form. When g is of type An,Bn,Cn or Dn, a sufficient condition for the irreducibility of standard parabolic baby Verma g-modules is obtained. This partially answers a question raised by Friedlander and Parshall (1990) in [2]. Moreover, as an application, in the special case that g is of type An or Bn, and χ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen (1999) in [6].",

keywords = "Maximal weight vector, Nilpotent orbit, Parabolic baby Verma module, Standard Levi form, Sub-regular nilpotent orbit",

author = "Li, \{Yi Yang\} and Bin Shu and Yao, \{Yu Feng\}",

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doi = "10.1016/j.jalgebra.2020.07.009",

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T1 - A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras

AU - Li, Yi Yang

AU - Shu, Bin

AU - Yao, Yu Feng

PY - 2020/12/1

Y1 - 2020/12/1

N2 - Let G be a connected, reductive algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G). In this paper, we study representations of g with a p-character χ of standard Levi form. When g is of type An,Bn,Cn or Dn, a sufficient condition for the irreducibility of standard parabolic baby Verma g-modules is obtained. This partially answers a question raised by Friedlander and Parshall (1990) in [2]. Moreover, as an application, in the special case that g is of type An or Bn, and χ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen (1999) in [6].

AB - Let G be a connected, reductive algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G). In this paper, we study representations of g with a p-character χ of standard Levi form. When g is of type An,Bn,Cn or Dn, a sufficient condition for the irreducibility of standard parabolic baby Verma g-modules is obtained. This partially answers a question raised by Friedlander and Parshall (1990) in [2]. Moreover, as an application, in the special case that g is of type An or Bn, and χ lies in the sub-regular nilpotent orbit, we recover a result of Jantzen (1999) in [6].

KW - Maximal weight vector

KW - Nilpotent orbit

KW - Parabolic baby Verma module

KW - Standard Levi form

KW - Sub-regular nilpotent orbit

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DO - 10.1016/j.jalgebra.2020.07.009

M3 - 文章

AN - SCOPUS:85089465052

SN - 0021-8693

VL - 563

SP - 111

EP - 147

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A criterion for irreducibility of parabolic baby Verma modules of reductive Lie algebras

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Keywords

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