334 reputation
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bio website euclid.unh.edu/~nikshych
location New Hampshire, USA
age 42
visits member for 5 years, 6 months
seen Jun 29 at 22:32
I am a Professor at the University of New Hampshire. I work on tensor categories, Hopf algebras, and quantum groups.

Mar
19
awarded  Nice Answer
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