All Questions
9 questions with no upvoted or accepted answers
9
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0
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254
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Decomposition of linear groups into free products
I recently learnt about Nagao's theorem which states $SL_2(k[t])\cong SL_2(k)\ast_{B(k)}B(k[t])$ for a field $k$. I read in "A.W. Mason, Serre's generalization of Nagao's theorem" that a theorem of ...
- 5,901
7
votes
0
answers
329
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A basic question on a base change of a homogeneous space of a linear algebraic group
I asked this basic question in MSE and got a comment "This belongs to Mathoverflow", so I ask my question here.
Let $G$ be a linear algebraic group over a field $k$, and $H\subset G$ be a $k$-...
- 14.2k
5
votes
0
answers
140
views
Classification of visible actions for *reducible* representations?
Is there a classification of the pairs $(G,V)$ such that $G$ is reductive [and connected, if you like], and $G$ acts faithfully and visibly on $V$ - crucially, including all cases where $V$ is ...
- 3,230
4
votes
0
answers
322
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Steinberg relations for elementary subgroup of a Chevalley group over an arbitrary ring
Given a semisimple Lie algebra $\frak{g}$ of type $\Phi$ with a Lie algebra representation $\rho:\frak{g}\to \frak{gl}(v)$ and an arbitrary commutative ring one can associate the following gadgets:
...
- 435
4
votes
0
answers
174
views
Algebraic varieties associated to finite groups
Have the following equations been studied in the literature?
Let $G$ be a finite group.
Then I am looking for functions $f : G \rightarrow \mathbb{C}~ \backslash \left\lbrace 0 \right\rbrace $ such ...
- 2,753
4
votes
0
answers
214
views
Hyperbolic subgroups of general linear groups
Is there a classification of hyperbolic subgroups of $GL_n(A)$ for $A$ some ring of characteristic $p$? $A$ for me is a finitely presented algebra over a finite field.
More precisely I'm looking for ...
- 5,901
3
votes
0
answers
233
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A bridge between the algebraic / differential geometry of $\frak{sl}_2(\mathbb{C})$ and the Sheffer-Appell calculus and combinatorics
In "Four examples of Beilinson-Bernstein localization", Anna Romanov introduces the basis
$m_k = \frac{(-1)^k}{k!} \partial^k \delta $
on p. 9, where $\partial$ is a partial derivative and $\...
- 10.5k
2
votes
0
answers
68
views
Centralizer/Normalizer of global sections of vector bundles on curves
Let $X$ be a smooth, projective curve of genus at least $2$ over $\mathbb{C}$ and $E$ be a vector bundle on $X$ of rank at least $2$. Given any point $x \in X$, denote by $S_x$ the image of the ...
- 1,981
0
votes
0
answers
303
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Automorphism group of algebraic function fields
Let $K$ be a finite field and let $F/K$ be a function field. Is it possible to deduce the genus of $F/K$ from the automorphism group of $G=Aut(F/K)$?
Is it possible to do so if we know that $|G|$ is ...
- 2,179