The peak algebra of the symmetric group revisited
نویسندگان
چکیده
منابع مشابه
The Peak Algebra of the Symmetric Group
The peak set of a permutation σ is the set {i : σ (i − 1) < σ (i) > σ (i + 1)}. The group algebra of the symmetric group Sn admits a subalgebra in which elements are sums of permutations with a common descent set. In this paper we show the existence of a subalgebra of this descent algebra in which elements are sums of permutations sharing a common peak set. To prove the existence of this peak a...
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The P-modular Descent Algebra of the Symmetric Group
The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the radical, and its nilpotency index. It also allows the irreducible representations of the descent algebra to be described.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2004.04.007