Semisimple Representations of Alternating Cyclotomic Hecke Algebras

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• 作者：Clinton Boys
• 关键词：Alternating groups ; Alternating Hecke algebras ; Khovanov ; Lauda ; Rouquier algebras ; Representation theory
• 刊名：Algebras and Representation Theory
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：19
• 期：1
• 页码：235-253
• 全文大小：530 KB
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• 作者单位：Clinton Boys (1)
  
  1. School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW, 2006, Australia
  
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079

文摘

We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman’s hash involution. We compute the rank of these algebras and construct a full set of irreducible representations in the semisimple case, generalising Mitsuhashi’s results Mitsuhashi (J. Alg. 240 535–558 2001, J. Alg. 264 231–250 2003).