Rings of invariants for three dimensional modular representations

Jürgen Herzog; Vijaylaxmi Trivedi

doi:10.1007/s00209-023-03350-2

Rings of invariants for three dimensional modular representations

Jürgen Herzog
, Vijaylaxmi Trivedi

Mathematics

University of Duisburg-Essen

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

Abstract

Let p> 3 be a prime number. We compute the rings of invariants of the elementary abelian p-group (Z/ pZ) ^r for 3-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersection rings with embedding dimension ⌈ r/ 2 ⌉ + 3 . This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for r= 3 , and was later proved for r= 4 by Pierron and Shank.

Original language	English
Article number	22
Journal	Mathematische Zeitschrift
Volume	305
Issue number	2
DOIs	https://doi.org/10.1007/s00209-023-03350-2
State	Published - Oct 2023

Keywords

Modular representations
Ring of invariants
SAGBI basis

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title = "Rings of invariants for three dimensional modular representations",

abstract = "Let p> 3 be a prime number. We compute the rings of invariants of the elementary abelian p-group (Z/ pZ) r for 3-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersection rings with embedding dimension ⌈ r/ 2 ⌉ + 3 . This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for r= 3 , and was later proved for r= 4 by Pierron and Shank.",

keywords = "Modular representations, Ring of invariants, SAGBI basis",

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N2 - Let p> 3 be a prime number. We compute the rings of invariants of the elementary abelian p-group (Z/ pZ) r for 3-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersection rings with embedding dimension ⌈ r/ 2 ⌉ + 3 . This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for r= 3 , and was later proved for r= 4 by Pierron and Shank.

AB - Let p> 3 be a prime number. We compute the rings of invariants of the elementary abelian p-group (Z/ pZ) r for 3-dimensional generic representations. Furthermore we show that these rings of invariants are complete intersection rings with embedding dimension ⌈ r/ 2 ⌉ + 3 . This proves a conjecture of Campbell, Shank and Wehlau in [CSW], which they proved for r= 3 , and was later proved for r= 4 by Pierron and Shank.

KW - Modular representations

KW - Ring of invariants

KW - SAGBI basis

UR - https://www.scopus.com/pages/publications/85171891299

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DO - 10.1007/s00209-023-03350-2

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VL - 305

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 2

M1 - 22

ER -

Rings of invariants for three dimensional modular representations

Abstract

Keywords

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