All Questions
3 questions
14
votes
2
answers
783
views
A question on invariant theory of $\mathrm{GL}_n(\mathbb{C})$
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Sym{Sym}$Let $\rho$ denote the irreducible algebraic representation of $\GL_n(\mathbb{C})$ with the highest weight $(2,2,\underset{n-2}{\underbrace{0,\...
- 63.9k
14
votes
1
answer
681
views
If an equivariant map is smooth on diagonal matrices, is it smooth everywhere?
This is a followup from a question I asked on math.SE, which received a helpful answer but unfortunately not a complete one. $\def\Sym{\mathrm{Sym}_{n\times n}}$
$\def\s{\mathrm{Sym}}\def\sp{\s^+}$Let ...
- 15.5k
6
votes
1
answer
589
views
Generalizing cosine rule to symmetric spaces
The sine and cosine rules for triangles in Euclidean, spherical and hyperbolic spaces can be understood as invariants for triples of lines. These invariants are given in terms of the distance (both ...
- 4,577