Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral

Understand

We consider the tensor power $V=(C^N)^{\otimes n}$ of the vector representation of $gl_N$ and its weight decomposition $V=\oplus_{\lambda=(\lambda_1,...,\lambda_N)}V[\lambda]$.

• For $\lambda = (\lambda_1 \geq ...
• \geq \lambda_N)$, the trivial bundle $V[\lambda]\times \C^n\to\C^n$ has a subbundle of q-conformal blocks at level l, where $l = \lambda_1-\lambda_N$ if $\lambda_1-\lambda_N> 0$ and l=1 if $\lambda_1-\lambda_N=0$.
• We construct a polynomial section $I_\lambda(z_1,...,z_n,h)$ of the subbundle.