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Jia-jun Ma's user avatar
Jia-jun Ma's user avatar
Jia-jun Ma's user avatar
Jia-jun Ma
  • Member for 13 years, 4 months
  • Last seen more than a week ago
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Closure order on nilpotent orbits in exceptional Lie algebras
I am curious about how Spaltenstein verify/construe such kind of diagrams? What's the algorithm to check $O_1 \subset \overline{O_2}$ without knowing the Hasse diagram a priori?
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A bijection between "symplectic" partitions and bi-partitions via Springer correspondance
I have the same question. How to describe the springer correspondence explicitly in terms of partition and symbols? Any reference?
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Erratum for Fulton and Harris
Thank you Bruce, Sheila Sundaram's thesis definitely extends my understanding on branching rules.
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Is $k[X]^G$ integral closed in $k[X]$.
Thanks for your answer!
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When the affine quotient is faithfully flat?
Thank you very much! You are right. The same computations of dimensions of null fiber shows that $m\geq 2n$ is the necessary conditions for the map $\phi$ to be faithfully flat.
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Why $G\to G/H$ is faithfully flat?
Here raise a question: if $G/H$ is quasi-affine, is $G/H$ locally trivial?
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Why $G\to G/H$ is faithfully flat?
Thank you very much for your answer! I have find a English book with a proof of faithfully flat: Section 5.7 in Jantzen's Representations of algebraic groups. For the locally trivial part. Yes, I means Zariski locally trivial as you said. I guess I may not be true in general. But it is quite interesting that although this is not true, by the faithfully flatness, the vector bundle $G\times_H V\to G/H$ is locally trivial, c.f. Secion~5.9 of Jantzen's book, where $V$ is a finite dimensional (over $k$) representation of $H$.
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