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On Norm Residue Symbols and Conductors

✍ Scribed by Romyar T Sharifi

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
131 KB
Volume
86
Category
Article
ISSN
0022-314X

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✦ Synopsis

Using the norm residue symbol and a reciprocity law of Artin and Hasse, we determine the conductors of Kummer extensions of the form K( p n a, n)Γ‚K(n) for any unramified extension K of Q p , element a # K*, and primitive p n th root of unity `n. We are able to do this without more recent and general reciprocity laws, which were needed in earlier proofs of the case K=Q p .

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Jantzen Seitz partitions are those p-regular partitions of n which label p-modular irreducible representations of the symmetric group S n which remain irreducible when restricted to S n&1 ; they have recently also been found to be important for certain exactly solvable models in statistical mechanic