Representations of symmetric groups with non-trivial determinant
نویسندگان
چکیده
A representation of a group is a realization of its elements in terms of matrices that takes the group operation into matrix multiplication. The groups of permutations (symmetric groups) were among the first families of groups for which the representations were classified in the work of Frobenius, Schur and Young around 1900. It was found that the irreducible representations of the nth permutation group are parametrized by integer partitions of n. Taking the determinant of the representing matrix results in either the trivial character, or in the sign character of the nth permutation group.
منابع مشابه
Partition complexes , duality and integral tree representations
We show that the poset of non-trivial partitions of {1, 2, . . . , n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σn and Σn+1 on the homology and cohomology of this partially-ordered set. AMS Classification 05E25; 17B60, 55P91
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 150 شماره
صفحات -
تاریخ انتشار 2017