2 problems

Affine denominator conjecture. The affine Macdonald denominator is given by

Let $J_{\mu,k,\mathsf{k}}(q,\lambda,\omega)=\chi_{\mu,k,\mathsf{k}}(q,\lambda,\omega)/\chi_{0,0,\mathsf{k}}(q,\lambda,\omega)$ be the affine Macdonald polynomial for…