ABSTRACT
U(n) Basic Hypergeometric Series Multiple series generalizations of basic hypergeometric series over the UNITARY GROUPS U(n1): The fundamental theorem of U(n) series takes c1; ..., cn and x1; ..., xn as indeterminates and n]1: Then
c1 cn; qð ÞN (q; q)N
X
Y
1 xr xs
1 xr xs
2 6664
3 7775
Yn
xr xs
cs; q
! yr
q xr xs
; q
! yr
2 666664
3 777775 q
;
where it is assumed that none of the denominators vanish (Bhatnagar 1995, p. 22). The series in this theorem is called an SU(n) series (Milne 1985; Bhatnagar 1995, p. 22).
