5
votes
1answer
90 views

Character Tables of $D_{4}$ and $Q_{8}$

Is there an intuitive reason that the Quaternion group and the Dihedral group on four vertices have the same character table? Does this indicate something special about the two groups? Or is it more ...
5
votes
0answers
52 views

Making modular representation theory and cohomology 'compelling' and 'accesible'

I'm currently putting together an application for a dissertation completion fellowship offered through my university. A part of the application includes 500-1000 words describing my dissertation. ...
0
votes
0answers
35 views

Clifford Theory Proof Representation Theory

I have a few questions about the proof of clifford theory and basic applications. Note: I am using that for class functions $\chi_1,\chi_2$ we have that $\langle \chi_1,\chi_2^x\rangle =\langle ...
4
votes
0answers
82 views

Representation Theory versus Galois Theory. [closed]

At my university there is a debate about whether it is better to require students to have taken a class in Galois theory or to require a class in representation theory for admission into the graduate ...
3
votes
0answers
77 views

Etymology of the term “weight vector”

I am writing a work on the representation theory of $SU(3)$ in basque and I would like to know the etymology of the term $\textbf{weight vector}$ in order to properly translate it.
0
votes
0answers
24 views

Characters and ''twisted dimensions''

Can someone shed some light at this part of wiki article about character theory: http://en.wikipedia.org/wiki/Character_theory#.22Twisted.22_dimension ? It kind of just stands there without any ...
3
votes
1answer
106 views

Real life applications of Maass wave forms

Explaining my work on Maass wave forms to friends and family (all non-mathematician) typically earns me blank faces. So I wonder whether there is some good example to explain their meaning to laymen. ...
2
votes
2answers
117 views

interesting topic about representation theory

I have to develop a discussion about representation theory (about 30 pages). My knowledge is very superficial and limited to general representations theory of groups and characters theory. Do you know ...
6
votes
2answers
90 views

Usefulness of induced representations.

I am learning representation theory from Serre's book by myself. Currently I am reading about induced representations, but I don't understand the importance. The concept looks strange and the ...
3
votes
1answer
112 views

bests book of representation theory for algebraic number theorists

I am looking for some of the best books on representation theory for an algebraic number theorists> I would prefer a book that is more number theoretical (e.g, galois representations, p adic ...
2
votes
3answers
108 views

Usefulness of the concept of equivalent representations

Definition: Let $G$ be a group, $\rho : G\rightarrow GL(V)$ and $\rho' : G\rightarrow GL(V')$ be two representations of G. We say that $\rho$ and $\rho'$ are $equivalent$ (or isomorphic) if $\exists ...
2
votes
2answers
220 views

Question regarding the definition of direct sum decomposition of a representation

Please bear with me. I am trying to learn representation theory of finite groups from J.P. Serre's book by myself. Here, the author has used the word 'representation' for the homomorphism $\rho : ...
10
votes
2answers
271 views

Path Algebra for Categories

For a while I had been thinking that the path algebra of a quiver $Q$ over a commutative ring $R$ is the same as the "category ring" $R[P]$ (analogous to "group ring", "monoid ring", "semigroup ring", ...
0
votes
1answer
113 views

Topic for presentation on Group Representations, Young Tableaux, Symmetric Group

I need to do a presentation relating to group representations/Young tableaux/symmetric group; however, for all my searching, I cannot find a cool topic that I find personally interesting (and that is ...
2
votes
0answers
110 views

DFT shift theorem generalizations?

The DFT shift theorem implies that any circular shift in the input space is equivalent to a phase change in the frequency domain, while the absolute values are preserved. $$ ...
5
votes
3answers
322 views

Looking for texts in representation theory

I recently finished a course in representation theory, and while I learned a lot from it, I know that there's a lot more in the subject that I missed. For the course we used Fulton and Harris as a ...
2
votes
2answers
94 views

Projective representations of loop groups

If $G$ is a Lie group and we take its loop group $LG$ why do we deal with projective representations of $LG$ and central extensions thereof? Where does the extra complexity come in to require us to ...
4
votes
1answer
114 views

An analogy between group actions and group represenations

I was trying to make a 'dictionary' between group action and group representation terms using the $\mathbb{C}[-]$ functor. I immediately found that if the set $Y \subset X$ is invariant under the ...
3
votes
1answer
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 ...
7
votes
1answer
473 views

Importance of Group Representation theory

I was reading about the group representation, but couldn't really why is it important or interesting. Can you someone explain about some of the important mathematical applications (not from physics, ...
31
votes
4answers
5k views

The Langlands program for beginners

Assuming that a person has taken standard undergraduate math courses (algebra, analysis, point-set topology), what other things he must know before he can understand the Langlands program and its ...