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14
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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 ...
14
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2
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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,\...
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6
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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 ...
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