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Results tagged with characteristic-p
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user 4231
Fields of characteristic $p$, i.e., fields for which there is a prime $p$ such that $px=0$ for each $x$. Do not use this tag for questions on characteristic polynomials of a matrix.
10
votes
1
answer
1k
views
Are there "reasonable" criteria for existence/non-existence of Levi factors or their conjuga...
Classical theorems attributed to Levi, Mal'cev, Harish-Chandra for a finite
dimensional Lie algebra over a field of characteristic 0 state that it has a Levi decomposition (semisimple subalgebra plus …
- 2,821
4
votes
Representations of $\mathrm{SL}(2)$ in characteristic 2
There is unfortunately no "formula" for tensor products in prime characteristic. Instead you can derive a list of composition factors $L(\lambda)$ (with multiplicity) by recursion. When $p=2$ there …
- 35.5k
2
votes
Automorphisms of Lie algebra of type $A_5$ modulo its center in characteristic 2
The answer is fairly classical (and no longer really at research level), but the most natural setting for it is the more general study of Lie algebras obtained by reduction mod $p$ from Chevalley's in …
- 52.9k
3
votes
Accepted
Branching rule for classical Lie algebras in positive characteristic
As my comment indicated, there is currently little hope of writing down general branching rules in characteristic $p$. In fact, given the history of work on Lusztig's conjecture about formal charact …
- 52.9k
3
votes
Quotient of a reductive group by a non-smooth subgroup
As xuhan points out, SGA3 provides a fairly comprehensive view of what can be said about quotients involving group schemes. The price of this thoroughness is of course a lengthy technical treatment …
- 52.9k
7
votes
Accepted
Dimension of irreducible representations in characteristic p
I'm not sure where you are starting in terms of background and references, but the standard short book for such questions is Serre's Linear Representations of Finite Groups (Springer GTM 42, a good En …
- 52.9k
11
votes
Accepted
On Category O in positive characteristic
Maybe I can answer the original question more directly, leaving aside the interesting recent geometric work discussed further in later posts like the Feb 10 one by Chuck: analogues of Beilinson-Bernst …
- 52.9k
6
votes
What is the correct formulation of the CDE triangle?
To revisit Bruce's earlier question, it might be useful to suggest a more sceptical alternative to Ben's answer and the related comments. I doubt that there will be a "correct" version of the CDE-tr …
- 52.9k