On character tables related to the alternating groups
نویسندگان
چکیده
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). 1. Preliminaries We fix a positive integer n. We will use the same notation as in [2], which we recall here. If μ = (μ1, μ2, . . .) is a partition of n we write μ ∈ P and then zμ denotes the order of the centralizer of an element of (conjugacy) type μ in Sn. Suppose μ = (1 1, 22, . . .), is written in exponential notation. Then we may factor zμ = aμbμ, where aμ = ∏
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