Related papers: Some questions about representations of p-adic gro…
We develop JSJ decomposition theory of pro-p groups.
In this paper, we survey some mathematical developments that followed from the discovery of simple supercuspidal representations of p-adic groups.
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.
Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…
Based on recent work of Kaletha, we apply Hakim--Murnaghan's result to study distinguished regular supercuspidal representations of tamely ramified reductive $p$-adic groups. Assuming $p$ is sufficiently large, we obtain a necessary and…
We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients…
We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.
We determine the characters of SL(2) representations of groups and surface groups.
This paper is dedicated to the study of the stability of multiplicities of group representations.
Quasirational presentations ($QR$-presentations) of (pro-$p$)groups are studied. Such presentations include, in particular, aspherical presentations of discrete groups and their subpresentations and pro-$p$-groups with a single defining…
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated
We consider lifting of mod p representations to mod p^2 representations in the setting of representations of (i) finite groups; (ii) absolute Galois groups of abstract fields; and (iii) absolute Galois groups of local and global fields.
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups $G$, a list of cuspidal $C$-types…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
Inspired by work surrounding Igusa's local zeta function, we introduce topological representation zeta functions of unipotent algebraic groups over number fields. These group-theoretic invariants capture common features of established…