2 problems

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The PBW filtration conjecture for vacuum representations of affine Kac–Moody algebras
About 19 years old
The PBW filtration conjecture. One has
openaffine-kac-moody-algebras pbw-filtration representation-theory
013
Cherednik–Orr conjecture on nonsymmetric Macdonald polynomials and PBW characters
At least 11 years old
Cherednik–Orr conjecture. Assume that $\la$ is an antidominant weight. Then
opendemazure-modules nonsymmetric-macdonald-polynomials pbw-filtration
05