All Questions
8 questions
8
votes
1
answer
295
views
What are twisted Verma modules? Basic properties?
Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbf{C}$, $\lambda$ be a weight in the nonnegative Weyl chamber and $w_1,w_2\in W$. Then the twisted Verma modules are defined e.g. in Andersen and ...
- 5,701
5
votes
0
answers
152
views
Concrete computation of pullback of the $D$-module $\mathbb{C}[t,t^{-1}]$
I have some problems in calculating some example explicitly. Consider
$$ \{0\} \overset{i}{\rightarrow} \mathbb{C} \overset{j}{\leftarrow} \mathbb{C}^*.$$
Then $Rj_+\mathbb{C}[t,t^{-1}] = \mathbb{C}[t,...
- 1,168
5
votes
1
answer
266
views
Two identities involving Ext functors in the context of D-modules
I have several questions regarding proposition 2.3 in "Cherednik and Hecke algebras of varieties with a finite group action", by Pavel Etingof. Let $X$ be a complex affine algebraic variety ...
- 541
6
votes
0
answers
275
views
The geometric "hands-on" vs. algebraic approach to nearby cycles
Feel free to skip to the question below; the following is just context and discussion:
An interesting, but seemingly less used result in the theory of nearby cycles of constructible sheaves is (...
- 272
3
votes
1
answer
312
views
Iterating specialization of sheaves?
This is a question about the operation of taking the specialization of sheaves along a subspace. I'll recall the settings in which I've encountered a notion of specialization of sheaves:
The real, ...
- 272
4
votes
0
answers
103
views
Computing $\mathcal D$-module direct image along group action map
Say everything is over $\mathbb C$, and I have an action $act: N \times X \to X$ of an affine algebraic group $N$ on a smooth variety, say with finitely many orbits. I'm trying to compute the $\...
- 403
-1
votes
1
answer
301
views
Is $\mathbb{P}^1$ the only smooth projective curve with a locally split tangent lie algebroid?
Let $C$ be a smooth projective curve over an algebraically closed field $k$.
The tangent lie algeborid $\mathcal{T}_C$ of $C$ is just sheaf of vector fields on $C$ equipped with the usual lie ...
- 7,789
12
votes
1
answer
842
views
What kind of algebraic object is $\mathcal{D}_X$? (algebra of diifferential operators). What's special about modules over it?
Let $R$ be a regular ring over a field of char 0. Let $X=Spec R$ and $D=\mathcal{D}_X$
the algebra of differential operators over it.
The overall vague question is what kind of algebraic object is $...
- 7,789