On permutation characters of wreath products |
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Authors: | Adalbert Kerber Jürgen Tappe |
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Institution: | Rheinisch Westfálische Technische Hochschule, Aachen, Federal Republic of Germany |
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Abstract: | It is known that the character rings of symmetric groups Sn and the character rings of hyperoctahedral groups S2?Sn are generated by (transitive) permutation characters. These results of Young are generalized to wreath products G?H (G a finite group, H a permutation group acting on a finite set). It is shown that the character ring of G?H is generated by permutation characters if this holds for G, H and certain subgroups of H. This result can be sharpened for wreath products G?Sn;if the character ring of G has a basis of transitive permutation characters, then the same holds for the character ring of G?Sn. |
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