10
votes
Accepted
Symmetric tensor of highest weight modules for $\mathrm{SU}(2)$
The multiplicities of $V_e$ inside $n$-th symmetric power of $V_d$ are given by the Cayley-Sylvester formula
$$
P(n,d;\frac{nd-e}{2}) - P(n,d;\frac{nd-e}{2}-1)
$$
where $P(n,d;k)$ denotes the number ...
- 8,149
7
votes
Question regarding the definition of linearization of line bundles
I think that you should regard the first definition as an imprecise version of the second definition. For example, suppose that $ X $ is a point and so $ L $ is simply a 1-dimensional vector space. ...
- 4,287
5
votes
Which algebraic groups are generated by (lifts of) reflections?
Let $M$ be a division algebra of degree 3 (i.e., dimension 9) over $\mathbf{Q}$ that splits over $\mathbf{R}$, and $M_1$ its norm 1 subgroup. So $M_1$ is a $\mathbf{Q}$-anisotropic simple algebraic ...
- 59.4k
2
votes
Quotients of schemes by connected groups
$\DeclareMathOperator\PGL{PGL}\DeclareMathOperator\GL{GL}$It seems that J. Kollár gave some examples in his paper "Non-quasi-projective moduli spaces".
In pg. 1080, I think that there is an ...
- 396
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