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

Fingerprint

Representation Theory
Littlewood-Richardson Coefficients
Orthogonality Relations
Schur Functions
Invariant Theory
Wreath Product
General Linear Group
Arbitrary
Character
Irreducible Representation
Symmetric group
Finite Group
Decompose
Subset
Class
Object

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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

The Extended k-Characters. / Johnson, Kenneth W.

Lecture Notes in Mathematics. Springer Verlag, 2019. p. 211-229 (Lecture Notes in Mathematics; Vol. 2233).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Johnson KW. The Extended k-Characters. In Lecture Notes in Mathematics. Springer Verlag. 2019. p. 211-229. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-030-28300-1_6