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For a complex character of a finite group , it is known that the product is a multiple of , where is the image of on . The character is said to be a sharp character of type if and . If the principal character of is not an irreducible constituent of , then the character is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups with normalized sharp characters of type . Here we prove that such a group with nontrivial center is...
We extend the notions of quasi-monomial groups and almost monomial groups in the framework of supercharacter theories, and we study their connection with Artin’s conjecture regarding the holomorphy of Artin -functions.
This work presents an approach towards the representation theory of the braid groups . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures on classical...
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