Generalizations of theq-Morris Constant Term Identity

Theq-Morris constant term identity gives the constant term in the Laurent polynomial expansion ofΦ≔∏Nl=1 (wl; q)a(q/wl; q)b∏1⩽j<k⩽N(wj/wk; q)λ (qwk/wj; q)λ. A conjecture is given for the constant term ofΦwhen multiplied by ∏N0+1⩽j<k⩽N(1−qλ(wj/wk))(1−qλ+1(wk/wj)). This conjecture is proved in the casesa=λ(generalN0,N1,b,λ),a=b=0 (generalN0,N1,λ), andN1=2 (generala,b,λ,N0), whereN0+N1=N. Also, a general identity relatingq-Morris-type constant terms andq-Selberg-type integrals is derived and is used to rewrite the conjecture as aq-Selberg-type integral evaluation.