The 2A-Majorana representations of the Harada-Norton group

Clara Franchi; Alexander A. Ivanov; Mario Mainardis

The 2A-Majorana representations of the Harada-Norton group

Clara Franchi, Alexander A. Ivanov, Mario Mainardis

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span $U$ of the Majorana axes. Finally, we prove that, if ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.

Lingua originale	English
pagine (da-a)	175-187
Numero di pagine	13
Rivista	Ars Mathematica Contemporanea
Volume	11
Stato di pubblicazione	Pubblicato - 2015

Keywords

ASSOCIATION SCHEMES
MAJORANA REPRESENTATIONS
MONSTER ALGEBRA

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title = "The 2A-Majorana representations of the Harada-Norton group",

abstract = "We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span $U$ of the Majorana axes. Finally, we prove that, if ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.",

keywords = "ASSOCIATION SCHEMES, MAJORANA REPRESENTATIONS, MONSTER ALGEBRA, ASSOCIATION SCHEMES, MAJORANA REPRESENTATIONS, MONSTER ALGEBRA",

author = "Clara Franchi and Ivanov, {Alexander A.} and Mario Mainardis",

year = "2015",

language = "English",

volume = "11",

pages = "175--187",

journal = "Ars Mathematica Contemporanea",

issn = "1855-3966",

publisher = "Ljubljana, Slovenia: SloveniaDru{\v s}tvo Matematikov, Fizikov in Astronomov Slovenije DMFA–zalo{\v z}ni{\v s}tvo",

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TY - JOUR

T1 - The 2A-Majorana representations of the Harada-Norton group

AU - Franchi, Clara

AU - Ivanov, Alexander A.

AU - Mainardis, Mario

PY - 2015

Y1 - 2015

N2 - We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span $U$ of the Majorana axes. Finally, we prove that, if ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.

AB - We show that all $2A$-Majorana representations of the Harada-Norton group $F_5$ have the same shape. If ${\mathcal R}$ is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span $U$ of the Majorana axes. Finally, we prove that, if ${\mathcal R}$ is based on the (unique) embedding of $F_5$ in the Monster, $U$ is closed under the algebra product.

KW - ASSOCIATION SCHEMES

KW - MAJORANA REPRESENTATIONS

KW - MONSTER ALGEBRA

KW - ASSOCIATION SCHEMES

KW - MAJORANA REPRESENTATIONS

KW - MONSTER ALGEBRA

UR - http://hdl.handle.net/10807/68917

M3 - Article

VL - 11

SP - 175

EP - 187

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

ER -