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Results tagged with rt.representation-theory
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user 22709
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
3
votes
0
answers
65
views
Historical appearance of using $\operatorname{SO}_3$-representation theory for spherical har...
$\DeclareMathOperator\SO{SO}$The spherical Laplace equation and the spherical harmonics are a beautiful example of a differential equation dominated by the representation theory of the Lie group of ro …
- 12.9k
11
votes
Examples of finite groups with "good" bijection(s) between conjugacy classes and irreducible...
I think it is one of the wunderful beauties of the representation theory of finite groups of Lie type $G(\mathbb{F_{p^n}})$ such as $GL_2(\mathbb{F_p})$ mentioned above, that irreducible representati …
- 1,846
3
votes
Restricting the Steinberg representation of $SL_{2n}$ over a finite field to the symplectic ...
This is also not a complete answer, but I think technically the right track: Paul Broussous already suggested in his answer to define the Steinberg representation by induction of parabolics and Jim Hu …
- 1,846
5
votes
2
answers
1k
views
symmetric 2-cocycle / many projective representations
Let $G$ be a finite group, $k$ the field of complex numbers.
Are there (cohomologically nontrivial) group 2-cocycles $\sigma\in Z^2(G,k^\times)$ such that for all $g,h\in G$:
$$\sigma(g,h)=\si …
- 1,846
3
votes
Non-Drinfeld–Jimbo deformations and finite quantum groups
Much depending on what you want to do with it.... ;-)
There is a duality between coordinate algebras to the Drinfel'd-Jimbo $U_q(\mathfrak{g})$ (you're title suggests you're interested rather in the …
- 1,846
1
vote
Commutator table for Chevalley group G_2
At first: sorry, I could't find the source you were looking for, but I'm so free to sketch two ways how you in my opinion get very fast to the informations you need (especially the latter, generic, mi …
- 1,846