# Tagged Questions

112 views

### Getting an intuitive feel for induced representations

I'm reading about induced representations for research. Particularly, I'm trying to get a firm grasp on the finite group case before venturing on to the locally compact case. I've been looking at ...
586 views

### Why are we interested in irreducible representation but not faithful representation?

I am reading some materials of representation theory (of a group). The motivation of representation theory is to represent (by a homomorphism $h: G \to GL(V)$, from the group $G$ to a vector space ...
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### Understanding analytic construction of induced representation

I'd like to get some intuition for analytic construction of induced representations as described on Wikipedia. Algebraic construction also described there is much more intuitive and clear to me, but ...
162 views

### How to understand $\frac{d}{dt}\{(\exp(tX))_*(Y)\}|_{t=0}=[X,Y]$?

Let $G$ be a Lie group on which $X$ and $Y$ are two vector fields. Let $G\xrightarrow{\exp(tX)} G$ be the (Lie theory) exponential map corresponding to $X$. Then of fundamental importance is ...
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### What to take from representation of $S_d$?

I am reading about group representations, and books I read all contain the representation theory for symmetric groups $S_d$. However none of them presents the material in a friendly way. After reading ...
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### Algebraic geometry in representation theory?

I heard that today algebraic geometry plays some significant role in representation theory, which is a little surprising because when I learnt representation theory it is basically algebra, topology, ...
425 views

### Intuition behind Maschke's theorem

I'm an undergraduate learning about group representations and Young tableaux, and have came across Maschke's theorem stating; If $G$ is a finite group and $F$ is a field who's characteristic does ...
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### What is a minimal polynomial of a group element, and why would we care if it was quadratic?

EDIT: the $p$-stable definition I give below is incorrect. I have included the correct definition as an answer to this question. I am trying to understand the definition of a p-stable group. The ...
1k views

### Understanding induced representations

Let $G$ be a group and $H$ be a subgroup. Let $\phi:H\rightarrow GL(V)$ be a representation of $H$. There are three constructions in Wikipedia, but I am not really convinced by these. My question is: ...
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### Something behind the substitution $h^0=\frac{1}{|G|}\sum_{t\in G}\rho^2_{t^{-1}}h\rho^2_{t}$?

I am quite new to representation theory and I reading Serre's Linear Representation of Finite Groups. In the first and second chapter, one trick he uses quite often is the substitution ...
201 views

### Intuition on the definition of “rational maps”

I'm studying some representation theory on $S_n$ and $GL(V)$ and tensor spaces, and have come across a lot of material involving rational representations. I'm not really an algebraic geometer by ...
Given a finite group $G$ and a field $K$, one can form the group ring $K[G]$ as the free vector space on $G$ with the obvious multiplication. This is very useful when studying the representation ...