A recursion for a symmetric function generalization of the q-Dyson constant term identity

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the q -Dyson constant term identity or Zeilberger–Bressoud theorem. The non-zero part Kadell's is indexed by weak composition v = ( 1 , … n ) in case when only one i ≠ 0 . This was first proved Károlyi, Lascoux and Warnaar 2015. They further formulated closed-form expression above mentioned all parts are distinct. Recently we obtained recursion this provided that largest occurs with multiplicity paper, generalize our previous result to compositions