@inbook{fb6a4ff9682e46f585a9ea14048708cc,

title = "The Extended k-Characters",

abstract = "The subject of this chapter is the k-characters χ(k) of a finite group G, and their extensions to more general objects. These characters are constant on certain subsets of Gk, the k-classes. Here work of Vazirani is presented which provides a set of “extended k-characters” for arbitrary k. These connect with various aspects of the representation theory of the symmetric groups and the general linear groups. Immanent k-characters are defined for arbitrary k and any irreducible representation λ of Sn. They coincide with the usual k-characters if λ is the sign character and in the cases k = 2 and k = 3 they had appeared with other names. There are connections with the representation theory of wreath products, with invariant theory and Schur functions. There are orthogonality relations and the Littlewood-Richardson coefficients appear in the decomposition of products of extended k-characters.",

author = "Johnson, {Kenneth W.}",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/978-3-030-28300-1_6",

language = "English (US)",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "211--229",

booktitle = "Lecture Notes in Mathematics",

address = "Germany",

}