### Abstract

Original language | English |
---|---|

Publisher | ArXiv |

Publication status | Submitted - 30 Oct 2018 |

### Fingerprint

### Keywords

- math.RT
- math.RA

### Cite this

*A proof of the first Kac-Weisfeiler conjecture in large characteristics*. ArXiv.

**A proof of the first Kac-Weisfeiler conjecture in large characteristics.** / Martin, Benjamin; Stewart, David; Topley, Lewis.

Research output: Working paper

}

TY - UNPB

T1 - A proof of the first Kac-Weisfeiler conjecture in large characteristics

AU - Martin, Benjamin

AU - Stewart, David

AU - Topley, Lewis

N1 - The third author is grateful for the support of EPSRC grant number EP/N034449/1.

PY - 2018/10/30

Y1 - 2018/10/30

N2 - In 1971, Kac and Weisfeiler made two influential conjectures describing the dimensions of simple modules of a restricted Lie algebra $\mathfrak{g}$. The first predicts the maximal dimension of simple $\mathfrak{g}$-modules and in this paper we apply the Lefschetz principle and classical techniques from Lie theory to prove this conjecture for all restricted Lie subalgebras of $\mathfrak{gl}_n(k)$ whenever $k$ is an algebraically closed field of characteristic $p \gg n$. As a consequence we deduce that the conjecture holds for the the Lie algebra of a group scheme when specialised to an algebraically closed field of almost any characteristic.

AB - In 1971, Kac and Weisfeiler made two influential conjectures describing the dimensions of simple modules of a restricted Lie algebra $\mathfrak{g}$. The first predicts the maximal dimension of simple $\mathfrak{g}$-modules and in this paper we apply the Lefschetz principle and classical techniques from Lie theory to prove this conjecture for all restricted Lie subalgebras of $\mathfrak{gl}_n(k)$ whenever $k$ is an algebraically closed field of characteristic $p \gg n$. As a consequence we deduce that the conjecture holds for the the Lie algebra of a group scheme when specialised to an algebraically closed field of almost any characteristic.

KW - math.RT

KW - math.RA

M3 - Working paper

BT - A proof of the first Kac-Weisfeiler conjecture in large characteristics

PB - ArXiv

ER -