Modular representations of strange classical Lie superalgebras and the first super Kac-Weisfeiler conjecture

Ye Ren; Bin Shu; Fanlei Yang; An Zhang

paper

Modular representations of strange classical Lie superalgebras and the first super Kac-Weisfeiler conjecture

arXiv:2307.00483

Abstract

Suppose $g = g_{0 ˉ} + g_{1 ˉ} i s a L i es u p er a l g e b r a o f q u eer t y p eor p er i pl ec t i c t y p eo v er ana l g e b r ai c a l l y c l ose df i e l d$ \textbf{k} $o f c ha r a c t er i s t i c$ p>2 $. I n t hi s a r t i c l e, w e ini t ia t e p r e l imina r i l y t o in v es t i g a t e m o d u l a r r e p r ese n t a t i o n so f p er i pl ec t i c L i es u p er a l g e b r a s an d t h e n v er i f y t h e f i r s t s u p er K a c - W e i s f e i l er co nj ec t u r eo n t h e ma x ima l d im e n s i o n so f i r r e d u c ib l e m o d u l es f or$ \mathfrak{g} $p r o p ose d b y t h eseco n d - nam e d a u t h or in [S h u] w h er e t h eco nj ec t u r e i s t a r g e t e d a t a l l f ini t e - d im e n s i o na l r es t r i c t e d L i es u p er a l g e b r a so v er$ \bk$, and already proved to be true for basic classical Lie superalgebras and completely solvable restricted Lie superalgebras.

19 pages. Comments are welcome