Related papers: Supercharacter theories and Schur rings
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular…
We establish new bounds on character values and character ratios for finite groups $G$ of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form…
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity…
For a finite group $G$ and complex character $\chi\in\mathrm{Irr}(G)$ that restricts irreducibly to a normal subgroup $N\vartriangleleft G,$ we prove a theorem about Clifford correspondences between the characters of subgroups of $G$ that…
Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…
We study relativized Lascar groups, which are formed by relativizing Lascar groups to the solution set of a partial type $\Sigma$. We introduce the notion of a Lascar tuple for $\Sigma$ and by considering the space of types over a Lascar…
In this paper, we prove a conjecture of Wei Zhang on comparison of certain local spherical characters from which we draw some consequences for the Ichino-Ikeda conjecture for unitary groups.
In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal Hamming distance and the group order. This is a generalized…
We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can be viewed as generalization of many well-known concepts, for example integrally closed ideals of finite colength and Cohen--Macaulay rings of minimal…
This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.
In a recent work [Das et al., Bull. Sci. Math. 199 (2025), 103580], the structure of characterized subgroups corresponding to arithmetic-type sequences was investigated. Building upon this work, we further show that a characterized subgroup…
This paper develops the theory of distinguished regular supercuspidal representations, and it highlights how the correspondence between regular characters and regular supercuspidal representations resembles induction in certain ways.
Let G be a finite group, and let E be a generalised cohomology theory, subject to certain technical conditions. We study a certain ring C(E,G) that is the best possible approximation to E^0BG that can be built using only knowledge of the…
In this note, we continue the investigation of the new version of characterized subgroups of the circle group $\mathbb{T}$, namely, "statistically characterized subgroups" (shortly, "s-characterized subgroups") recently introduced in…
P. Das, A. Ghosh and T. Aziz has given in \cite[Theorem 3.15]{ADG} a result on statistically characterized subgroups of the circle group $\mathbb{R}/\mathbb{Z}$, which answers, together with \cite[Corollary 2.4]{DG24}, questions of…
A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…
Very recently, in [Das et al., J. Lond. Math. Soc., 2025], statistically characterized subgroups were studied for certain classes of non-arithmetic sequences. Subsequently, in [Das et al., Bull. Sci. Math., 2025], characterized subgroups…
We explore the possibilities for constructing Lagrangian descriptions of three-dimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields. Classes of such theories with N…