Isomorphism between Systems of Equivariant Singularities

Xiaofeng Wang; Duo Wang; Yun Tang

doi:10.1006/jmaa.1998.5996

Isomorphism between Systems of Equivariant Singularities

Xiaofeng Wang^*
, Duo Wang
, Yun Tang

^*Corresponding author for this work

Tsinghua University
Peking University

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

1 Citation (Scopus)

Abstract

In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system ofO(n)-equivariant singularities in its irreducible representation on Rⁿis isomorphic to that of one-dimensional Z₂-equivariant singularities and the system of[formula]-dimensionalO(n)-equivariant singularities is isomorphic to that ofn-dimensionalS_n-equivariant singularities.

Original language	English
Pages (from-to)	26-45
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	225
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.1998.5996
Publication status	Published - 1 Sept 1998
Externally published	Yes

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10.1006/jmaa.1998.5996

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title = "Isomorphism between Systems of Equivariant Singularities",

abstract = "In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system ofO(n)-equivariant singularities in its irreducible representation on Rnis isomorphic to that of one-dimensional Z2-equivariant singularities and the system of[formula]-dimensionalO(n)-equivariant singularities is isomorphic to that ofn-dimensionalSn-equivariant singularities.",

author = "Xiaofeng Wang and Duo Wang and Yun Tang",

note = "Funding Information: * This work is supported by NNSF of China.",

year = "1998",

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AU - Wang, Duo

AU - Tang, Yun

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PY - 1998/9/1

Y1 - 1998/9/1

N2 - In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system ofO(n)-equivariant singularities in its irreducible representation on Rnis isomorphic to that of one-dimensional Z2-equivariant singularities and the system of[formula]-dimensionalO(n)-equivariant singularities is isomorphic to that ofn-dimensionalSn-equivariant singularities.

AB - In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system ofO(n)-equivariant singularities in its irreducible representation on Rnis isomorphic to that of one-dimensional Z2-equivariant singularities and the system of[formula]-dimensionalO(n)-equivariant singularities is isomorphic to that ofn-dimensionalSn-equivariant singularities.

UR - https://www.scopus.com/pages/publications/0040082983

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DO - 10.1006/jmaa.1998.5996

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VL - 225

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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Isomorphism between Systems of Equivariant Singularities

Abstract

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