Séminaire Lotharingien de Combinatoire, B52c (2004), 8 pp.

Christine Bessenrodt and Jørn B. Olsson

On Character Tables Related to the Alternating Groups

Abstract. There is a simple formula for the absolute value of the determinant of the character table of the symmetric group Sn. It equals aP, the product of all parts of all partitions of n (see [4, Corollary 6.5]). In this paper we calculate the absolute values of the determinants of certain submatrices of the character table X of the alternating group An, including that of X itself (Section 2). We also study explicitly the powers of 2 occurring in these determinants using generating functions (Section 3).

Received: May 7, 2004. Accepted: October 1, 2004.

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