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Here is an answer from a mathematician who prefers me to post it here myself:
Harish-Chandra bimodules make sense in a very wide context. Take two
filtered algebras A, A' that quantize the same ...

Here is an answer by Gwyn Bellamy, which he let me post here:
1) Is there a conjecture on the classification of symplectic resolutions? No, not that I am aware of. I think this is the wrong ...

This is close to Balazs's answer. $X$ is the nilpotent cone for $SL(2)$. The Springer resolution $T^* \mathbb P^1 \to X$ is semismall. $T^* \mathbb P^1$ is the total space of the line bundle $O(-2)$ ...

Sorry, I remembered how to answer my own question. Consider the degree of a HN stratum as a Young diagram with rational lengths of rows. It is enough to show that the Young diagram of A is a subset of ...

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