Submatrices of character tables and basic sets

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 introduced by Lapointe and Morse. Arithmetic properties of the numbers occurring in this context are studied via generating functions.Comment: 18 pages; examples added, typos removed, some further minor changes, references update

Residue symbols and Jantzen-Seitz partitions

Jantzen-Seitz partitions are those $p$-regular partitions of~$n$ which label $p$-modular irreducible representations of the symmetric group $S_n$ which remain irreducible when restricted to $S_{n-1}$; they have recently also been found to be important for certain exactly solvable models in statistical mechanics. In this article we study their combinatorial properties via a detailed analysis of their residue symbols; in particular the $p$-cores of Jantzen-Seitz partitions are determined

Restriction of Odd Degree Characters of Sn\mathfrak{S}_n

Let $n$ and $k$ be natural numbers such that $2^k < n$. We study the restriction to $\mathfrak{S}_{n-2^k}$ of odd-degree irreducible characters of the symmetric group $\mathfrak{S}_n$. This analysis completes the study begun in [Ayyer A., Prasad A., Spallone S., Sem. Lothar. Combin. 75 (2015), Art. B75g, 13 pages] and recently developed in [Isaacs I.M., Navarro G., Olsson J.B., Tiep P.H., J. Algebra 478 (2017), 271-282]

Participation, inclusion and belonging. The importance of trust while integrating newly arrived immigrant children in a Swedish primary school.

This thesis investigates the importance of trust while integrating newly arrived immigrant children in a Swedish primary school located in a municipality where several neighbourhoods can be considered segregated. The research question is for this reason: "Is trust important while integrating newly arrived children in school and what does the trust building process look like?" Pupils, mainly newly arrived, teachers and other school personnel are interviewed. The data is analysed through theories of trust. The study concludes that trusting relationships in the school, involving teachers, peers, and parents are crucial for integration

Complex group algebras of the double covers of the symmetric and alternating groups

We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\geq 5$ be an integer, $G$ a finite group, and let \AAA and \SSS^\pm denote the double covers of \Al_n and \Sy_n, respectively. We prove that \CC G\cong \CC \AAA if and only if G\cong \AAA, and \CC G\cong \CC \SSS^+\cong\CC\SSS^- if and only if G\cong \SSS^+ or \SSS^-. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.Comment: 27 pages, the previous version is revised slightly, to appear in Algebra & Number Theor

Restriction of odd degree characters of Sn

Let n and k be natural numbers such that 2k < n. We study the restriction to Sn−2k of odd-degree irreducible characters of the symmetric group Sn. This analysis completes the study begun in [Ayyer A., Prasad A., Spallone S., Sém. Lothar. Combin. 75 (2015), Art. B75g, 13 pages] and recently developed in [Isaacs I.M., Navarro G., Olsson J.B., Tiep P.H., J. Algebra 478 (2017), 271-282]

Kvinnor med utländsk bakgrund i vårdyrken

Sociologen Wuokko Knockes forskning från 1986 påvisade hur kvinnor med utländsk bakgrund diskriminerades på den svenska arbetsmarknaden. Det rådde arbetskraftsbrist inom industrin under denna period vilket bidrog till att invandrarkvinnor ofta blev hänvisade till denna sektor, och där blev tilldelade de mest lågvärderade, tyngsta och enformigaste arbetsuppgifterna, och inom den offentliga sektorn fick kvinnorna de mest lågbetalda och minst stimulerade arbetena. Syftet med denna undersökning är att undersöka om kvinnor med utländsk bakgrund fortfarande upplever diskriminering inom den offentliga vården och hur den i så fall beskrivs. Det råder idag arbetskraftsbrist inom den offentliga sjukvården (Knocke 2011:225-226) och det är därför intressant att se hur detta eventuellt påverkar trivseln och arbetsdelningen på arbetsplatsen. Mitt empiriska material har vissa likheter med Knockes forskning. Materialet påvisar att utomeuropeiska/muslimska kvinnor upplever diskriminering vid enstaka tillfällen eller mer systematiskt i sitt arbete på sin arbetsplats, medan kvinnor från andra länder i Europa eller med utomeuropeisk bakgrund men som är födda eller uppvuxna i Sverige inte upplever diskriminering från sina chefer eller kollegor

Generalized hook lengths in symbols and partitions

In this paper, we present, for any integer d, a description of the set of hooks in a d-symbol. We then introduce generalized hook length functions for a d-symbol, and prove a general result about them, involving the core and quotient of the symbol. We list some applications, for example to the well-known hook lengths in integer partitions. This leads in particular to a generalization of a relative hook formula for the degree of characters of the symmetric group discovered by G. Malle and G. Navarro in [3]