All Questions
Tagged with dual-pairs rt.representation-theory
5 questions
28
votes
4
answers
2k
views
Matrices: characterizing pairs $(AB, BA)$
Let $A$ be an $m\times n$-matrix and $B$ an $n \times m$-matrix over the same field. Consider the matrices $C=AB$ and $D=BA$. It is probably well known (and not difficult to show) that the only ...
10
votes
2
answers
1k
views
How to decompose a composition of representations?
Background
I would like to know if there is some slick machinery to solve the following representation-theoretic problem.
Let $\left(V,\langle-,-\rangle\right)$ be a finite-dimensional real inner ...
5
votes
3
answers
5k
views
Spherical Harmonics - a bunch of questions about them
Hi there,
Please tell me if I should divide these into individual questions next time.
Short intro:
Spherical Harmonics are a nice collection of functions. They are orthogonal and allow you to take ...
6
votes
2
answers
1k
views
Which tensor fields on a symplectic manifold are invariant under all Hamiltonian vector fields?
Consider a connected symplectic manifold $(M, \omega)$ of dimension $m=2n$. A few preliminary reminders (mostly to fix the notation): A vector field $X$ is symplectic if its flow preserves the ...
5
votes
2
answers
1k
views
Howe duality for exceptional algebras
There is a nice tool in representation theory, the Howe duality, which as I know works for certain pairs of classical Lie algebras (the reference to the complete list of Howe dual pairs is appreciated ...