Abstract
Abstract. Let H ⊆ G be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic p > 0. In our first principal theorem we show that if a closed subgroup K of H is H-completely reducible, then it is also G-completely reducible in the sense of Serre, under some restrictions on p, generalising the known case for G = GL(V ). Our second main theorem shows that if K is H-completely reducible, then the saturation of K in G is completely reducible in the saturation of H in G (which is again a connected reductive subgroup of G), under suitable restrictions on p, again generalising the
known instance for G = GL(V ). We also study saturation of finite subgroups of Lie type in G. Here we generalise a result due to Nori from 1987 in case G = GL(V ).
known instance for G = GL(V ). We also study saturation of finite subgroups of Lie type in G. Here we generalise a result due to Nori from 1987 in case G = GL(V ).
Original language | English |
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Publisher | ArXiv |
DOIs | |
Publication status | Published - 30 Jan 2024 |
Bibliographical note
The research of this work was supported in part by the DFG (Grant#RO 1072/22-1 (project number: 498503969) to G. R¨ohrle).
Keywords
- math.RT
- math.GR
- 20G15, 14L24