Irreducibility conjecture for the quotient representations of the double affine Hecke algebra

Let $I^{(k,r)}_m$ be the ideals in the polynomial representation $V$ of the double affine Hecke algebra representation $\mathcal{H}_n^{(k,r)}$, with $I^{(k,r)}_{m-1}\subset I^{(k,r)}_m$. Irreducibility conjecture. The quotient representations

$$I^{(k,r)}_m/I^{(k,r)}_{m-1}$$

are irreducible. This asserts irreducibility of the successive subquotients in the filtration by ideals associated with the $(k,r)$ wheel condition; the supplied text gives no resolution or further conditions beyond the surrounding construction.