Bessenrodt, Christine; Olsson, Jørn B. On character tables related to the alternating groups. (English) Zbl 1068.20012 Sémin. Lothar. Comb. 52, B52c, 8 p. (2004). Summary: There is a simple formula for the absolute value of the determinant of the character table of the symmetric group \(S_n\). It equals \(a_{\mathcal P}\), the product of all parts of all partitions of \(n\) [see G. D. James, The representation theory of the symmetric groups. (Lect. Notes Math. 682) (1978; Zbl 0393.20009), Corollary 6.5]. In this paper we calculate the absolute values of the determinants of certain submatrices of the character table \(\mathcal X\) of the alternating group \(A_n\), including that of \(\mathcal X\) itself (Section 2). We also study explicitly the powers of 2 occurring in these determinants using generating functions (Section 3). Cited in 2 Documents MSC: 20C30 Representations of finite symmetric groups 05E10 Combinatorial aspects of representation theory Keywords:determinants of character tables; symmetric groups; partitions; alternating groups; generating functions Citations:Zbl 0393.20009 PDFBibTeX XMLCite \textit{C. Bessenrodt} and \textit{J. B. Olsson}, Sémin. Lothar. Comb. 52, B52c, 8 p. (2004; Zbl 1068.20012) Full Text: EuDML EMIS