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This is a question about the second point in Geordie Williamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false?What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

This is a question about the second point in Geordie Williamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

This is a question about the second point in Geordie Williamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

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This is a question about the second point in Geordie Willamson'sWilliamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

This is a question about the second point in Geordie Willamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

This is a question about the second point in Geordie Williamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?

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The coxeter number condtion in the quantum Lusztig conjecture

This is a question about the second point in Geordie Willamson's answer in

What to do now that Lusztig's and James' conjectures have been shown to be false? ,

which says that the Lusztig conjecture doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?