The Extended k-Characters

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages211-229
Number of pages19
DOIs
StatePublished - Jan 1 2019

Publication series

NameLecture Notes in Mathematics
Volume2233
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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  • Cite this

    Johnson, K. W. (2019). The Extended k-Characters. In Lecture Notes in Mathematics (pp. 211-229). (Lecture Notes in Mathematics; Vol. 2233). Springer Verlag. https://doi.org/10.1007/978-3-030-28300-1_6