Cyclotomic Wenzl Algebras
Cyclotomic Wenzl Algebras
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发表时间：
2005
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通讯作者：
S. Ariki;Andrew Mathas;H. Rui
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作者：
S. Ariki;Andrew Mathas;H. Rui
纳扎罗夫[Naz 96]在研究布劳尔代数时引入了一种无限维代数，他称之为仿射温兹尔代数。本文研究了这类代数的某些分圆代数。我们构造了这些代数在一般情况下的不可约表示，并用它来证明这些代数是无秩r（2n − 1）的！！(whenΩ是u-可容许的）。接下来我们证明了这些代数是胞腔的，并给出了任意域上的分圆Wenzl代数的单模的标号。在乔治·卢斯蒂格教授60岁生日之际
Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank r(2n − 1)!! (when Ω is u– admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Wenzl algebras over an arbitrary field. On the occasion of Professor George Lusztig’s 60 birthday