Brauer algebras of simply laced type
Brauer algebras of simply laced type
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DOI：
10.1007/s11856-009-0095-9
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发表时间：
2007-04
影响因子：
1
通讯作者：
A. Cohen;Bart J. Frenk;D. B. Wales
中科院分区：
文献类型：
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作者：
A. Cohen;Bart J. Frenk;D. B. Wales
Brauer引入的图代数描述了正交李群的自然表示的叠张量积的中心化代数，它由仅依赖于路径图an - 1onn - 1节点的生成器和关系表示。这里我们描述了一个依赖于任意图q的代数，称为类型为q的Brauer代数，并研究了它的结构，在这种情况下，q是一个简单带球面型的Coxeter图（因此它的连通成分是类型为an−1，Dn, E6, E7, E8）。我们找到了它的不可约表示及其维数，并证明了它是元胞代数。该代数是一般的半简单代数，并且包含类型为q_coxeter群的群代数为子代数。它是q型的Birman-Murakami-Wenzl代数的环同态象；这一事实将在以后的工作中用于确定简单带球面型Birman-Murakami-Wenzl代数的结构。
The diagram algebra introduced by Brauer that describes the centralizer algebra of then-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph An− 1onn− 1 nodes. Here we describe an algebra depending on an arbitrary graphQ, called the Brauer algebra of typeQ, and study its structure in the cases whereQis a Coxeter graph of simply laced spherical type (so its connected components are of type An− 1, Dn, E6, E7, E8). We find its irreducible representations and its dimension, and show that the algebra is cellular. The algebra is generically semisimple and contains the group algebra of the Coxeter group of typeQas a subalgebra. It is a ring homomorphic image of the Birman-Murakami-Wenzl algebra of typeQ; this fact will be used in later work determining the structure of the Birman-Murakami-Wenzl algebras of simply laced spherical type.