The Murnaghan-Nakayama rule and some virtual S_n characters
英文摘要:
We construct certain virtual characters for the symmetric groups, then compute a formula which calculates the values of these virtual characters.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Amitai Regev
We construct certain virtual characters for the symmetric groups, then compute a formula which calculates the values of these virtual characters.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of the complex reflection groups G(r,p,n)
复反射群$G(r,p,n)$的无穷级数的Iwahori-Hecke代数是最近由Ariki和Koike,Broué和Malle,以及Ariki的工作中构造的.本文给出了计算这类代数的不可约特征标的Murnaghan-Nakayama型公式。我们的方法是在我们的早期文件中,我们得出的Murnaghan-Nakayama规则的经典外尔群的Iwahori-Hecke代数的字符的推广。在这两篇论文中,我们都受到了C。Greene,他通过对Young正规表示中的对角矩阵元素求和,给出了不可约对称群特征标的Murnaghan-Nakayama公式的新推导。我们使用Ariki和Koike给出的$G(r,p,n)$的Iwahori-Hecke代数的类似表示。
We derive a Murnaghan--Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai's explicit decomposition of Lusztig restriction. We use our formula to show that most complex irreducible characters vanish on some $\ell$-singular element for certain primes $\ell$. As an application we classify the simple endotrivial modules of the finite quasi-simple classical groups. As a further application we show that for finite simple classical groups and primes $\ell\ge3$ the first Cartan invariant in the principal $\ell$-bl…
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Given natural numbers m and n, we define a deflation map from the characters of the symmetric group S_{mn} to the characters of S_n. This map is obtained by first restricting a character of S_{mn} to the wreath product S_m \wr S_n, and then taking the sum of the irreducible constituents of the restricted character on which the base group S_m \times ... \times S_m acts trivially. We prove a combinatorial formula which gives the values of the images of the irreducible characters of S_{mn} under this map. We also prove an analogous result for more general deflation maps in which the base group is…
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