Symmetries of the WDVV equations and Chazy-type equations

Ruud Martini; Gerhard F. Post

Symmetries of the WDVV equations and Chazy-type equations

Ruud Martini
, Gerhard F. Post

Discrete Mathematics and Mathematical Programming

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Abstract

We investigate the symmetry structure of the WDVV equations. We obtain an $r$-parameter group of symmetries, where $r = (n^2 + 7n + 2)/2 + \lfloor n/2 \rfloor$. Moreover it is proved that for $n=3$ and $n=4$ these comprise all symmetries. We determine a subgroup, which defines an $SL_2$-action on the space of solutions. For the special case $n=3$ this action is compared to the $SL_2$-symmetry of the Chazy equation. For $n=4$ and $n=5$ we construct new, Chazy-type, solutions.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente
Number of pages	8
Publication status	Published - 1998

Publication series

Name	Memorandum / Department of Applied Mathematics
Publisher	University of Twente, Department of Applied Mathematics
No.	1466
ISSN (Print)	0169-2690

Keywords

EWI-3286
MSC-35Q99
MSC-81T40
MSC-17B66
IR-65655
MSC-35N05
METIS-141310

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Cite this

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title = "Symmetries of the WDVV equations and Chazy-type equations",

abstract = "We investigate the symmetry structure of the WDVV equations. We obtain an \$r\$-parameter group of symmetries, where \$r = (n\textasciicircum{}2 + 7n + 2)/2 + \textbackslash{}lfloor n/2 \textbackslash{}rfloor\$. Moreover it is proved that for \$n=3\$ and \$n=4\$ these comprise all symmetries. We determine a subgroup, which defines an \$SL\_2\$-action on the space of solutions. For the special case \$n=3\$ this action is compared to the \$SL\_2\$-symmetry of the Chazy equation. For \$n=4\$ and \$n=5\$ we construct new, Chazy-type, solutions.",

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author = "Ruud Martini and Post, \{Gerhard F.\}",

note = "Imported from MEMORANDA",

year = "1998",

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente",

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TY - BOOK

T1 - Symmetries of the WDVV equations and Chazy-type equations

AU - Martini, Ruud

AU - Post, Gerhard F.

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - We investigate the symmetry structure of the WDVV equations. We obtain an $r$-parameter group of symmetries, where $r = (n^2 + 7n + 2)/2 + \lfloor n/2 \rfloor$. Moreover it is proved that for $n=3$ and $n=4$ these comprise all symmetries. We determine a subgroup, which defines an $SL_2$-action on the space of solutions. For the special case $n=3$ this action is compared to the $SL_2$-symmetry of the Chazy equation. For $n=4$ and $n=5$ we construct new, Chazy-type, solutions.

AB - We investigate the symmetry structure of the WDVV equations. We obtain an $r$-parameter group of symmetries, where $r = (n^2 + 7n + 2)/2 + \lfloor n/2 \rfloor$. Moreover it is proved that for $n=3$ and $n=4$ these comprise all symmetries. We determine a subgroup, which defines an $SL_2$-action on the space of solutions. For the special case $n=3$ this action is compared to the $SL_2$-symmetry of the Chazy equation. For $n=4$ and $n=5$ we construct new, Chazy-type, solutions.

KW - EWI-3286

KW - MSC-35Q99

KW - MSC-81T40

KW - MSC-17B66

KW - IR-65655

KW - MSC-35N05

KW - METIS-141310

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Symmetries of the WDVV equations and Chazy-type equations

PB - University of Twente

CY - Enschede

ER -