Simple modules as submodules and quotients of symmetric powers

János Kollár; Pham Huu Tiep

doi:10.1016/j.jalgebra.2024.05.020

Simple modules as submodules and quotients of symmetric powers

János Kollár, Pham Huu Tiep

Mathematics

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

1 Scopus citations

Abstract

Let G be any finite group, F any field, and V any finite-dimensional, faithful FG-module. If W is any irreducible FG-module, we show that there is an integer 1≤m≤|G| (depending on W) such that, for any integer k≥0, W is both a submodule and a quotient of Sym^m+k|G|(V).

Original language	English (US)
Pages (from-to)	286-291
Number of pages	6
Journal	Journal of Algebra
Volume	657
DOIs	https://doi.org/10.1016/j.jalgebra.2024.05.020
State	Published - Nov 1 2024

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Irreducible representations
Symmetric powers

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10.1016/j.jalgebra.2024.05.020

Cite this

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title = "Simple modules as submodules and quotients of symmetric powers",

abstract = "Let G be any finite group, F any field, and V any finite-dimensional, faithful FG-module. If W is any irreducible FG-module, we show that there is an integer 1≤m≤|G| (depending on W) such that, for any integer k≥0, W is both a submodule and a quotient of Symm+k|G|(V).",

keywords = "Irreducible representations, Symmetric powers",

author = "J{\'a}nos Koll{\'a}r and Tiep, {Pham Huu}",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

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doi = "10.1016/j.jalgebra.2024.05.020",

language = "English (US)",

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T1 - Simple modules as submodules and quotients of symmetric powers

AU - Kollár, János

AU - Tiep, Pham Huu

PY - 2024/11/1

Y1 - 2024/11/1

N2 - Let G be any finite group, F any field, and V any finite-dimensional, faithful FG-module. If W is any irreducible FG-module, we show that there is an integer 1≤m≤|G| (depending on W) such that, for any integer k≥0, W is both a submodule and a quotient of Symm+k|G|(V).

AB - Let G be any finite group, F any field, and V any finite-dimensional, faithful FG-module. If W is any irreducible FG-module, we show that there is an integer 1≤m≤|G| (depending on W) such that, for any integer k≥0, W is both a submodule and a quotient of Symm+k|G|(V).

KW - Irreducible representations

KW - Symmetric powers

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DO - 10.1016/j.jalgebra.2024.05.020

M3 - Article

AN - SCOPUS:85195093075

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VL - 657

SP - 286

EP - 291

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Simple modules as submodules and quotients of symmetric powers

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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