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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 …
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 …
David Roberts's user avatar
  • 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 …
Jim Humphreys's user avatar
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 …
Jim Humphreys's user avatar
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 …
Jim Humphreys's user avatar
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 …
Jim Humphreys's user avatar
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 …
Jim Humphreys's user avatar
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 …
Jim Humphreys's user avatar