Submatrices of character tables and basic sets

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In this investigation of character tables of nite groups we study basic
sets and associated representation theoretic data for complementary sets of conjugacy lasses. For the symmetric groups we nd 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 dened by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions
TidsskriftJournal of Combinatorial Theory, Series A
Udgave nummer8
Sider (fra-til)1744-1788
Antal sider15
StatusUdgivet - 2012

ID: 40290171