Submatrices of character tables and basic sets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Bessenrodt, Christine¹  Olsson, Jorn B.² 

[1] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany

[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen O, Denmark

关键词: Character tables;    Basic sets;    Symmetric groups;    Determinants;    Cartan matrices;    Generating functions;    k-Schur functions;   

DOI  :  10.1016/j.jcta.2012.06.001

来源: Elsevier

【 摘 要 】

In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on restricted sets of conjugacy classes, like beautiful combinatorial determinant formulae for submatrices of the character table and Cartan matrices with respect to basic sets: we observe that similar phenomena occur for the transition matrices between power sum symmetric functions to bounded partitions and the k-Schur functions defined by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free