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Results tagged with lattices
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user 8857
Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
4
votes
Accepted
A lattice in $ \operatorname{SL}_n $ is Ad-irreducible
Per the request to post it as an answer.
Notice that the Ad representation is a polynomial representation into $\operatorname{GL}(\operatorname{Lie}(G))$.
We do know that $\operatorname{Ad}(G)$ acts i …
- 2,459
1
vote
How large is the set of unimodular lattices whose sucesssive minima cannot be attained by a ...
Edit 2 - Definitely the set of lattices spanned by their shortest vectors is of positive measure. … Edit - the answer below is about well-rounded lattices, which are particular kind of lattices spanned by their shortest vectors... …
- 2,459
1
vote
Accepted
Lattices in $p$-adic groups
Here's one example that I like.
Consider
$\Gamma = \{g \in SL_d\left[\sqrt{-m} / p\right] \mid g^t \cdot g^\sigma= I \}$, where $\sigma$ is the Galois conjugate. Then this is an arithmetic lattice in …
- 2,459