Double centralizing theorem for wreath products of the alternating group

Abstract

The double centralizing theorem between the action of the symmetric group S_n and the action of the general linear group on the tensor space T_n(W) was obtained by Schur. Here we obtain a double centralizing theorem when S_n is replaced by the wreath product of a finite group G and the alternating group A_n.

Keywords:

• Alternating group
• double centralizing property
• symmetric group
• wreath product

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20G05

Acknowledgements

The author would like to thank A. Regev for posing this problem and useful discussions and the Weizmann Institute of Science, where the main part of this research was done, for its hospitality.

Additional information

Funding

Supported by the Russian Foundation for Basic Research grant no. 16-01-00756.