# Tagged Questions

**1**

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107 views

### Non invertibility of certain integral arising from group action

Let a compact topological group $G$ with invariant measure $\mu,$ acts on a simply connected compact topological space $X$ and $\rho$ is a $n$-dimensional unitary representation of $G$. ...

**3**

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107 views

### Non-linearly isomorphic non-equivalent $G-$representations?

Let $G$ be an algebraic group (or a group scheme) over a field $\Bbbk$, and let $V$ be an algebraic $G-$representation (I mean, corresponding to a homomorphism of $\Bbbk-$group schemes $G\rightarrow ...

**0**

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**0**answers

93 views

### Actions and representations of profinite groups

Let $p$ be a prime number, and denote by $\mathbb{Z}_p$ the additive profinite group of p-adic integers. Let $G$ be a finitely generated profinite group of order coprime to $p$, and $V = ...

**2**

votes

**1**answer

91 views

### From the representation category of a Lie group and the representation on a homogeneous space, can we reconstruct the stabiliser subgroup reps?

Given a Lie group $G$ and a transitive action $- \triangleright - : G \times X \to X$ on a homogeneous space, we can recover the stabiliser subgroup $H_x$ of a point $x \in X$. It is the subgroup of ...

**2**

votes

**1**answer

126 views

### Tensor Powers of 1-Dimensional Representations of a Finite Group

Let $G$ be a finite group acting on a commutative ring $R$ via ring maps. In doubt, one can assume $R$ to be noetherian or regular if one wants. Let $P$ be a $1$-dimensional free $R$-module with a ...

**4**

votes

**1**answer

150 views

### Representations of Finite Subgroups on Homology

Suppose that $G$ is a connected, simply-connected, complex, semisimple Lie group, and that $H$ is finite subgroup. Consider the left-multiplicative action of $H$ on $G$, and the resulting ...

**1**

vote

**1**answer

451 views

### Actions of $Z_n$ and actions of $Z_{n-1}$

I am playing with some questions concerning connections between
certain poset partitions and their linear extensions. This is not
my usual playground, I just happened to stumble upon something.
When ...

**3**

votes

**2**answers

331 views

### Orbits of a symplectic group on its Lie algebra in the finite field case

The classical problem regarding the action of symplectic group on its Lie algebra gives rise to the following question in the finite field case.
Let $\mathbb F_p$ be a finite field. Then the ...