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Results tagged with rt.representation-theory
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user 22878
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
24
votes
2
answers
2k
views
Irreducible Degrees and the Order of a Finite Group
This is a question of aesthetics.
For a finite group of order $n$, the proof that the degree $d$ of a complex irreducible representation divides $n$ goes by showing that the rational number $n/d$ …
- 2,583
5
votes
0
answers
123
views
Are the canonical actions on Schubert Cells Linearizable?
G. Schwarz constructed a (counter)example for an action of a simple algebraic group on an affine space that is not linearizable (i.e., it is not a representations).
Natural examples of af …
- 2,583
4
votes
Closed orbits of complete flags in $\mathbb{C}^n$
$O(n)$, by definition preserves the bilinear forms. Consider a subspace $W_r$ of dimension $r$ where the form is zero for any pair of vectors. Put it as the $r$th term of a complete flag $F$. Now con …
- 2,583
3
votes
Representation theory of infinite dihedral group
It is a guess. Possibly what is meant is that the polynomial is palindromic: algebraically this means whenever $\alpha$ is a root $\alpha^{-1}$ is also a root, which translates to $f(x) = x^m f(\frac …
- 2,583
1
vote
0
answers
67
views
Relation Among Conjugacy Classes
This is more a request to find out if there is any work in the literature
discussing certain things.
Is there a naturally defined partial ordering on the set of conjugacy classes of a finite group G? …
- 2,583
-2
votes
1
answer
327
views
Is there any Lefschetz-like principle for representations of finite groups?
Representation theory (at least the origin of this terminology) aims to exhibit a model (a represetative) in the group of matrices for an abstract group which is known by only its group law. So compl …
- 2,583