5 papers
On power sum kernels on symmetric groups
Iskander Azangulov, Viacheslav Borovitskiy, Andrei Smolensky
In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups . Such processes are bi-invariant: the action…
The centralizers of root subgroups in Kac-Moody Steinberg groups
Andrei Smolensky
For the affine and hyperbolic root system the symmetric part of the centralizers of root subgroups in the corresponding Steinberg groups are calculated. In the affine case the corr…
Suzuki-Ree groups and Tits mixed groups over rings
Andrei Smolensky
It is shown that Suzuki-Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This elimina…
On the definition of Suzuki groups over rings
Andrei Smolensky
The definition of Suzuki groups over rings is given by means of an explicit description as a difference-algebraic group. For a (not necessarily perfect) field with more than two el…
Products of Sylow subgroups in Suzuki and Ree groups
Andrei Smolensky
An explicit and elementary proof is given to the fact that Suzuki and Ree groups can be decomposed into the product of 4 of their Sylow p-subgroups, where p is the defining charact…