论文标题
$ q $ -Dyson常数项身份的对称函数概括的递归
A recursion for a symmetric function generalization of the $q$-Dyson constant term identity
论文作者
论文摘要
在2000年，卡德尔（Kadell）对$ q $ -Dyson常数术语身份或Zeilberger--Bressoud $ q $ -Dyson Theorem的对称函数概括提出了正交性猜想。 Kadell正交性猜想的非零部分是一个稳定的项标识，在只有一个$ v_i \ neq 0 $的情况下，弱组成$ v =（v_1，\ dots，v_n）$。这一猜想最初是由Károlyi，Lascoux和Warnaar在2015年证明的。在$ V $的所有部分都不同的情况下，他们进一步为上述恒定术语制定了封闭式表达式。最近，我们获得了这个常数术语的递归，前提是$ v $的最大部分在$ v $中以多重性发生。在本文中，我们将以前的结果推广到所有构图$ v $。
In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the $q$-Dyson constant term identity or the Zeilberger--Bressoud $q$-Dyson theorem. The non-zero part of Kadell's orthogonality conjecture is a constant term identity indexed by a weak composition $v=(v_1,\dots,v_n)$ in the case when only one $v_i\neq 0$. This conjecture was first proved by Károlyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above mentioned constant term in the case when all the parts of $v$ are distinct. Recently we obtain a recursion for this constant term provided that the largest part of $v$ occurs with multiplicity one in $v$. In this paper, we generalize our previous result to all compositions $v$.
