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 $v_i\ne 0$. 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 obtained 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 weak compositions v.

在2000年，Kadell对q -Dyson常数项恒等式或Zeilberger-Bressoud q -Dyson定理的对称函数泛化给出了一个正交性猜想。Kadell正交性猜想的非零部分是一个常数项恒等式，该恒等式由弱组合索引$v=（v_{\mathrm{1个}}，\dots ，v_{ñ}）$ 如果只有一个 $v_{\mathrm{一世}}\ne 0$。这种猜想最早是由Károlyi，Lascoux和Warnaar于2015年证明的。在v的所有部分都不同的情况下，他们进一步为上述常数项制定了闭式表达式。最近，我们得到了这个常数项的递归，条件是v的最大部分出现在v中的多重性为1 。在本文中，我们将先前的结果推广到所有弱组合v。