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Algebra Seminar Wednesday at 2PM in H705
On a question of Feit (Robert Boltje, Sept.18, 2024)
In 1979 Feit asked the following question: Let χ be an irreducible character of a finite group G and let $n$ be the conductor of χ, i.e., the smallest positive integer $n$ such that all values of χ can be expressed as a rational linear combination of $n$-th roots of unity. Does this force G to have an element of order $n$?
Feit's question has been answered positively for solvable groups in 1986 by Ferguson and Turull, and independently by Amit and Chillag. Little progress has been made in the following decades. This talk reports on recent advances on this question in joint work with Alexander Kleshchev, Gabriel Navarro and Pham Huu Tiep.