微分算子与$B_n$型反射群
Differential operators and reflection group of type $B_n$
摘要：
本文研究了$B_n$型有限反射群$W$的量子Olshanetsky-Perelomov系统的多项式表示.我们赋予多项式环${\mathbb C} [x_1,\ldots\\\ldots, x_n]$一种在Weyl代数上的模结构，该模结构与$B_n$型反射群$W$下的不变多项式环${\mathbb C} [x_1,\ldots,x_n]^{W}$相关联.然后研究了反射群$W$下不变微分算子环的多项式表示。我们使用组表示论即与反射组$W$，并建立一个分解的结构，明确提供简单的组件的发电机。
英文摘要：
In this note, we study the polynomial representation of the quantum Olshanetsky-Perelomov system for a finite reflection group $W$ of type $B_n$. We endow the polynomial ring ${\mathbb C} [x_1,\ldots\\\ldots, x_n]$ with a structure of module over the Weyl algebra associated with the ring ${\mathbb C} [x_1,\ldots,x_n]^{W}$ of invariant polynomials under a reflections group $W$ of type $B_n$. Then we study the polynomial representation of the ring of invariant differential operators under the reflections group $W$. We use the group representation theory namely the higher Specht polynomials associated with the reflection group $W$ and establish a decomposition of that structure by providing explicitly the generators of the simple components.
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