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