Jeff Adler
  • Member for 11 years, 10 months
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Restriction of irreducible representations from $G(\mathbb Q_p)$ to $[G, G](\mathbb Q_p)$
Accepted answer
5 votes

I won't say anything here about the number of components in your restricted representation, but here is some information about multiplicities. Kwangho Choiy and Dipendra Prasad have (independently) ...

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Most harmful heuristic?
8 votes

Two bad principles that taste worse together: Decimals are the true numbers. Rounding makes no difference. Since students learn about decimals after they've learned about whole numbers and fractions,...

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Classification of automorphism groups of groups of order $p^4$
7 votes

Here's a description of the groups of order $p^4$. It's kind of primitive and explicit, but it's not too long.

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Conjugacy for $p$-adic matrices of finite order
2 votes

Here is a proof in the case where $p \not |m$ that doesn't involve modular representations, though it does involve a result of Gelfand and Kazhdan whose proof I can't remember, so I have no idea ...

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Irreducible representations of the unitriangular group
2 votes

An earlier answer tells you what happens when $n=3$. This is a special case of the Heisenberg group (at least in odd characteristic; not sure otherwise), any exposition of which might be illuminating ...

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What notions are used but not clearly defined in modern mathematics?
13 votes

The set of equivalence classes of irreducible, smooth representations of a reductive $p$-adic group $G$ should be partitioned into finite subsets called $L$-packets. Each $L$-packet should correspond ...

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Is restriction of scalars of simply connected algebraic groups still SC?
Accepted answer
3 votes

May I assume that $K/k$ is separable? Let $T$ be a maximal torus in $G$. Since $G$ is simply connected, the weight lattice and character lattice for $T$ are the same. This remains true if we ...

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Can breadth hurt a job candidate?
8 votes

Whether breadth is considered to be negative or positive will depend on the kind of job for which you are applying. For example, consider a high-powered research department looking for someone in ...

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maximal compact subgroup as fixed points of some involution on p-adic group?
6 votes

Here is how the real and p-adic situations are the same. Let $G$ be a connected reductive algebraic group defined over a field $F$ not of characteristic two. Let $\theta$ be an involution of $G$ ...

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