Since the beginning of this century the development of group theory has been dominated by the notion of representation, and the seemingly more specialized theory of group actions (permutations) has been given short shrift. To be sure, every action of a group can be considered as a particular representation by matrices, but in this setting some of the finer structure of the original permutations...

We formally analyze a computational problem which has important applications in image understanding and shape analysis. The problem can be summarized as follows. Starting from a group action on a Riemannian manifold M , we introduce a modification of the metric by partly expressing displacements on M as an effect of the action of some group element. The study of this new structure relates to ev...

In this paper we define a cyclic analogue of the MFS-action on derangements, and give a combinatorial interpretation of the expansion of the n-th derangement polynomial on the basis {qk(1 + q)n−1−2k}, k = 0, 1, . . . , b(n− 1)/2c.

We discuss some consequences of the braid group action on a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations along a face.