319 reputation
26
bio website euclid.unh.edu/~nikshych
location New Hampshire, USA
age 41
visits member for 4 years, 10 months
seen Nov 14 at 13:40
I am a Professor at the University of New Hampshire. I work on tensor categories, Hopf algebras, and quantum groups.

Sep
22
asked Outer group automorphisms preserving conjugacy classes of pairs of commuting elements
Sep
22
awarded  Autobiographer
May
3
awarded  Necromancer
Mar
6
comment Outer automorphisms of Borel subgroup
Thanks, Aakumadula ! Probably one can deduce that $\theta$ (modulo an inner automorphism) respects root subgroups by using that normal abelian subgroups of $B$ are in bijection with positive roots (at least for the type $A_n$). In particular, maximal normal abelian subgroups of $B$ correspond to simple roots. The automorphism $\sigma'$ of $B$ given by composition of taking transpose w.r.t (1n) -- (n1) diagonal and taking the inverse. Does this coincide with your $\sigma$? (it corresponds to the symmetry of the $A_n$ Dynkin diagram).
Mar
5
comment Outer automorphisms of Borel subgroup
Thanks! Sure $B$ coincides with its normalizer in $GL(n, F)$. But it appears that there are non-trivial outer automorphisms of $B$ , e.g., coming from automorphisms of $F$. Also, in this paper deepblue.lib.umich.edu/handle/2027.42/30473 the group $Out(B)$ is computed when $F$ is the field of $2$ elements. It is surprisingly large (in this case, of course, $B$ is the group of unipotent upper-triangular matrices)
Mar
5
revised Outer automorphisms of Borel subgroup
added 11 characters in body
Mar
5
revised Outer automorphisms of Borel subgroup
edited body
Mar
5
comment Outer automorphisms of Borel subgroup
Hi Jon! nice to see you here.
Mar
5
awarded  Student
Mar
5
asked Outer automorphisms of Borel subgroup
Jan
6
awarded  Yearling
Jun
2
awarded  Critic
May
29
answered Semisimple Hopf algebras with commutative character ring
May
28
answered Monoidal structures on von Neumann algebras
May
28
awarded  Editor
May
28
revised Non-symmetric Braiding on finite group Representation Categories
deleted 106 characters in body
May
28
comment Non-symmetric Braiding on finite group Representation Categories
Victor is right. I will edit the above answer.
May
28
awarded  Supporter
May
28
answered Non-symmetric Braiding on finite group Representation Categories
Jan
5
awarded  Teacher