Representations of Hecke Algebras and Characters of Symmetric Groups
Representations of Hecke Algebras and Characters of Symmetric Groups
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赫克代数的表示和对称群的特征
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发表时间：
2003
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通讯作者：
S. Donkin
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作者：
S. Donkin
考虑A型Hecke代数H（n）在本原l次单位根上的表示理论，其中l是正整数（不一定是素数）.我们给H（n）-模赋予一个“Brauer特征标”。这是对称群Sn的l-正则元素集合上的类函数。我们证明了一个类似的布劳尔的正交关系。作为字符分配的一个应用，我们证明了Cartan矩阵的行列式整除l的幂。Brundan和Kleshchev最近得到了这个行列式的精确公式。它们特别证明了这是l的幂，验证了A的一个猜想。Mathas
We consider the representation theory of a Hecke algebra H(n) of type A at a primitive lth root of unity, where l is a (not necessarily prime) positive integer. We assign a “Brauer character” to an H(n)-module. This is a class function on the set of l-regular elements of the symmetric group S n . We prove an analogue of Brauer’s orthogonality relations. As an application of the assignment of characters we show that the determinant of the Cartan matrix divides a power of l. A precise formula for this determinant has recently been obtained by Brundan and Kleshchev. They show in particular that this is a power of l, verifying a conjecture of A. Mathas.