I'd like to know how people prefer to write permutations, or elements of the symmetric group $S_n$ for $n\ge0$. The most natural way to define a permutation in $S_n$ is as a bijection on the set $\{1,2,....,n\}$. Then the set of permutations (bijections) becomes a group under composition of maps...

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory o...

Mathematics is rife with the fruit of abstraction. Many problems which first are solved via "direct" methods (long and difficult calculations, tricky estimates, and gritty technical theorems) later turn out to follow beautifully from basic properties of simple devices, though it often takes some...