A q - analogue of the type A Dunkl operator and integral kernel

A q-analogue of the type A Dunkl operator and integral kernel We introduce the q-analogue of the type A Dunkl operators, which are a set of degree–lowering operators on the space of polynomials in n variables. This allows the construction of raising/lowering operators with a simple action on non-symmetric Macdonald polynomials. A bilinear series of non-symmetric Macdonald polynomials is introduced as a q-analogue of the type A Dunkl integral kernel K A (x; y). The aforementioned operators are used to show that the function satisfies q-analogues of the fundamental properties of K A (x; y).