Let $p_1, p_2, \ldots$, be the power sum symmetric functions. Let $p_n^* = n \frac{\partial}{\partial p_n}$. Then $$ p_n^* p_m  p_m p_n^* = \delta_{m, n} 1. $$ Where could I find this result in some books or papers? Thank you very much.

In Nakajima's annals paper on the homlogy of Hilbert Schemes and the representation theorx of the Heisenberg algebra. This is also in his book on Hilbert schemes of points in chapter 8. 


Here is a PhD thesis on representations of the infinite dim. Heisenberg group. 

