Theoretical Statistics and Mathematics Unit, ISI Delhi

June 10, 2015 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Neha Hooda,
Indian Statistical Institute, Delhi

Title:
Mod-2 invariants and subgroup embeddings of algebraic groups

Abstract of Talk

Let $G$ be a simple linear algebraic group defined over a
field $k.$ It is an important problem to know what are all the
simple $k$-subgroups of $G$ as well as the number of such
subgroups required to generate $G$ over $k.$ In the talk we
try to answer this for algebraic groups of type $A_2,$ $G_2,$
$D_4$ and $F_4.$ More precisely, in the talk we will address
two problems. The first is to understand conditions that control
$k$-embedding of algebraic groups of type $A_1$ and $A_2$ in
simple groups of type $G_2$ and $F_4$ and the second is to
understand $k$-embedding of rank-2 tori in simple groups of
type $A_2,$ $G_2$ and $F_4.$ This study is done via the mod-2
invariants attached to these groups. The second problem is to
find the number of $k$-subgroups of a fixed Cartan-Killing
type as well as number of rank-2 k-tori required to generate
the groups of type $A_2,$ $G_2$ and $F_4$ over $k.$