Generalizations of the q-Morris constant term identity

The q-Morris constant term identity gives the constant term in the Laurent polynomial expansion of phi:= IIl=1N(w(t);q)(a)(q/w(l);q)(b)II1 less than or equal to j < k less than or equal to N(w(j)/w(k);q)(lambda)(qw(k)/w(j);q)(lambda). A conjecture is given for the constant term of phi when multiplied by IINO+1 less than or equal to j < k less than or equal to N(1-q(lambda)(w(j)/w(k)))(1-q(lambda)+1(w(k)/w(j))). This conjecture is proved in the cases a = lambda (general N-0, N-1, b, lambda), a = b = O (general N-0, N-1, lambda), and N-1 = 2 (general a, b, lambda, N-0), where N-0+N-1 = N. Also, a general identity relating q-Morris-type constant terms and q-Selberg-type integrals is derived and is used to rewrite the conjecture as a q-Selberg-type integral evaluation. (C) 1998 Academic Press.