On the minimal norm of a non-regular generalized character of an arbitrary finite group

Details On the minimal norm of a non-regular generalized character of an arbitrary finite group On the minimal norm of a non-regular generalized character of an arbitrary finite group

2009-02-08

arxiv.org/abs/0902.1312v2

Mathematics

Representation Theory

7 pages

Scientific paper

We prove that for any finite group G, the sum across non-identity elements of
the squared absolute value of any generalized character of G which does not
vanish on all non-identity elements of G is at least |G|/d -1, where d is the
maximal degree of a complex irreducible character of G, and we identify all
cases where this minimum possible value is attained.

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