Bailey type summation formulas associated with the root system \(F_4^{\lor}\)
In the paper under review the authors prove three basic hypergeometric summation formulas of Bailey type, associated with the root system \(F_4^\vee\) and involving a related Jackson integral. The first of these formulas, that they call \((1,1)\) case, is equivalent to the \(q\)-Macdonald-Morris constant term identity that was proved by \textit{F. G. Garvan} [SIAM J. Math. Anal. 21, No.~3, 803--821 (1990; Zbl 0711.33001)] and \textit{F. G. Garvan} and \textit{G. Gonnet} [Bull. Am. Math. Soc., New Ser. 24, No.~2, 343--347 (1991; Zbl 0737.33011); J. Symb. Comput. 14, No.~2--3, 141--177 (1992; Zbl 0766.33017)] and was subsequently generalizated to all root systems by \textit{I. Cherednik} [Ann. Math. (2) 141, No.~1, 191--216 (1995; Zbl 0822.33008)]. The authors go further and prove two new summation formulas that they call case \((2,0)\) and case \((0,2)\). They also prove, for the root system \(F_4^\vee\), that this kind of formula exists only in the above mentioned three cases.
scientific article; zbMATH DE number 5382255