All Questions
7 questions with no upvoted or accepted answers
4
votes
0
answers
219
views
Map $\operatorname{Sym}^{mp}(V^*) \longrightarrow K^{q}$ defined by $q$ points in $\operatorname{Sym}^p(V)$
EDIT : I have edited the question and made it more specific with respect to the kind of answer I expect.
Let $V$ be a finite dimensional $K$-vector space and let $x_1, \dotsc, x_q \in V$ be $q$ points,...
- 7,300
4
votes
0
answers
164
views
Matrices in $SL(2,\mathbb{C})$ with characteristic polynomial defined over a subring
Let $R\subset\mathbb{C}$ be a subring, and let $A,B\in SL(2,\mathbb{C})$ be matrices such that $A,B,AB$ all have trace in $R$.
For which $R$ can we then deduce that $A,B$ are simultaneously conjugate ...
- 7,527
2
votes
0
answers
101
views
On the irreducible submodules of adjoint representations $\text{ad}^{0}$
Let $k$ be a finite field of characteristic $p$. Let $H$ be a subgroup of $\rm{GL}_{n}(k)$ of order prime to $p$ where $n\geq2$. Assume that the representation $H\hookrightarrow \rm{GL}_{n}(k)$ is ...
- 667
2
votes
0
answers
75
views
Constructing representations of a topological group from characteristic polynomials of a generating set
Given a topological group $G$ and a subset $S$ of $G$ that topologically generates it, what are the conditions under which an $n$-dimensional continuous linear representation of $G$ over an ...
- 21
2
votes
0
answers
51
views
Relations among hyperplane mirror symmetries
Let $H(n) \subset O(n)$ be the set of mirror symmetries in $\mathbb{R}^n$ with respect to $(n - 1)$-planes containing the origin. One can see that for any $a, b, c \in H(2)$ we have $abcabc = id$, ...
- 5,590
2
votes
0
answers
63
views
Determining subgroup of finite group of Lie type from characteristic polynomials
Suppose you have $G$ a finite group of Lie type (say $\mathrm{Sp}_4( \mathbb{F}_5)$ as a case I particularly care about, but there are others.) Your friend picks a subgroup $H$ and selects random ...
- 2,429
1
vote
0
answers
206
views
About the question "Tannaka–Krein duality"
I saw this post recently: Tannaka–Krein duality
I have this question please: in the following which I report here:
The problem is with surjectivity: let us denote $\mathcal{G}:=\mathcal{G}(\mathcal{R}...
- 29