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Results tagged with lie-groups
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user 6827
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
4
votes
Borel–Weil theorem - reference request
Chapter II.5 in Jantzen's Representations of Algebraic Groups offers an algebraic treatment of this theorem.
- 3,702
3
votes
Accepted
Closed subgroups of $Tr_1(d,\mathbb{Q}_p)$
Pick $\lambda \in \mathbb{Z}_p \backslash \mathbb{Q}$ and define
$H = \left\lbrace\begin{pmatrix} 1 & 0 & a
\cr 0 & 1 & \lambda a \cr 0 & 0 & 1 \end{pmatrix} : a \in \mathbb{Z}_p\right\rbrace$.
Th …
- 3,702
2
votes
Accepted
Lower bound on the degree of a product of elements in a hyperalgebra/enveloping algebra
I don't have a full answer, but the following calculation may be useful.
Consider the example $G = SL_3$ so that $N$ is the Heisenberg group on three generators and in characteristic zero, $\bar{U}(N …
- 3,702
7
votes
What would you want on a Lie theory cheat poster?
Description of the fibres of the Springer resolution. Classification of nilpotent orbits.