The character table of the Iwahori-Hecke algebra of the symmetric group: Starkey's rule

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• 作者：Geck ; Meinolf
• 刊名：Comptes Rendus de l'Academie des Sciences Series I Mathematics
• 出版年：1999
• 出版时间：September 1, 1999
• 年：1999
• 卷：329
• 期：5
• 页码：361-366
• 全文大小：321 K

文摘

We consider the symmetric group G_n (regarded as a Coxeter group) and the corresponding Iwahori-Hecke algebra H_q(G_n). In 1975, Starkey introduced the character table of H_q(G_n) and gave an elegant rule for determining that table, in terms of the ordinary character table of G_n. We give a new simple proof of that rule, whose main ingredients are the exterior powers of the reflection representation of G_n and, otherwise, only general properties of Coxeter groups.