论文标题
在$ g型的循环组合hecke代数的半效率基碱基和双静态基础上（\ ell，1，n）$
On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type $G(\ell,1,n)$
论文作者
论文摘要
本文研究了半正态基础$ \ {f _ {\ Mathfrak {s} \ Mathfrak {t}}} \} $和双静态基础$ \ {g _ {g _ {\ mathfrak {s}} $ {h} _ {\ ell，n} $ g（\ ell，1，n）$的$。我们为常数提供了一些明确的公式，$α_ {\ Mathfrak {s} \ Mathfrak {t}}}}：= G _ {\ Mathfrak {\ Mathfrak {s} \ Mathfrak {t}}}}}}}}/f _ {\ Mathfrak {\ Mathfrak {\ Mathfrak { $γ$ -COEFFICINTS $ \ {γ_ {\ Mathfrak {u}}，γ'_ {\ Mathfrak {u}}} \} $ of $ h _ {\ ell，n} $。特别是，我们回答了Mathas关于某些$γ$ excefficients产品的平方根的合理性的问题。我们获得了一些明确的公式，用于扩展$ h _ {\ ell，n-1} $的每个阳性基础，作为$ h _ {\ ell，n} $ seminoral基础的线性组合，在自然包含$ h _ {\ ell，n-1} \ ell，n-1} \ hookfirtarrowh h _ _ _ _} $ n}下
This paper studies the seminormal bases $\{f_{\mathfrak{s}\mathfrak{t}}\}$ and the dual seminormal bases $\{g_{\mathfrak{s}\mathfrak{t}}\}$ of the non-degenerate and the degenerate cyclotomic Hecke algebras ${H}_{\ell,n}$ of type $G(\ell,1,n)$. We present some explicit formulae for the constants $α_{\mathfrak{s}\mathfrak{t}}:=g_{\mathfrak{s}\mathfrak{t}}/f_{\mathfrak{s}\mathfrak{t}}\in K^\times$ in terms of the $γ$-coefficients $\{γ_{\mathfrak{u}}, γ'_{\mathfrak{u}}\}$ of $H_{\ell,n}$. In particular, we answer a question of Mathas on the rationality of square roots of some quotients of products of $γ$-coefficients. We obtain some explicit formulae for the expansion of each seminormal bases of $H_{\ell,n-1}$ as a linear combination of the seminormal bases of $H_{\ell,n}$ under the natural inclusion $H_{\ell,n-1}\hookrightarrow H_{\ell,n}$.
