Related papers: Algebraic analysis of minimal representations
Minimal representations of a real reductive group G are the "smallest" irreducible unitary representations of G. The author suggests a program of global analysis built on minimal representations from the philosophy: small representation of…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…
En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…
We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number…
How does an irreducible representation of a group behave when restricted to a subgroup? This is part of branching problems, which are one of the fundamental problems in representation theory, and also interact naturally with other fields of…
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
This short paper being devoted to some aspects of the inverse problem of the representation theory treats several themes, which have their origins in the researches of F.A.Berezin, D.P.Zhelobenko, V.P.Maslov and his group, in context of the…
The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…