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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