How can we show that $$\sum_{n = 0}^\infty q^n \operatorname{char}_T S^n(\mathbb C[x,y])= \prod_{p_1,p_2\geq 0}\frac{1}{1-t_1^{p_1}t_2^{p_2}q}$$ where $\operatorname{char}_T V$ denotes the character of a representation $V$ of the torus $T$, and $T$ acts on $x,y$ as $(t_1,t_2)$?
References: proposition 2.1 and above eq. (4.5)