Arithmetic of characters of generalized symmetric groups |
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Authors: | D Joyner |
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Institution: | (1) Mathematics Department, US Naval Academy, Annapolis, Maryland, USA |
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Abstract: | The result here answers the following questions in the affirmative: Can
the Galois action on all abelian (Galois) fields $K/\mathbb{Q}$ be realized
explicitly via an action on characters of some finite group? Are all
subfields of a cyclotomic field of the form $\mathbb{Q}(\chi)$, for some
irreducible character $\chi$ of a finite group G? In particular, we
explicitly determine the Galois action on all irreducible characters of
the generalized symmetric groups. We also determine the smallest
extension of $\mathbb{Q}$ required to realize (using matrices) a given
irreducible representation of a generalized symmetric group.
Received: 18 February 2002 |
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Keywords: | Primary 20C15 20C30 Secondary 11R32 |
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