Related papers: Introduction to representation theory
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
We study and classify representations of a torsion group $G$ over an idempotent semifield with special attention on the case over the Boolean semifield $\mathbb{B}$. In subsequent work we extend this theory to studying representations of…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has…
This article is based on my lecture notes from summer schools at the Universities of Utah (June 2007) and Warwick (September 2007). We provide an introduction to explicit methods in the study of moduli spaces of quiver representations and…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…
The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used…
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
Logical relations (LR) have been around for many years, and today they are used in many formal results. However, it can be difficult to LR beginners to find a good place to start to learn. Papers often use highly specialized LRs that use…
We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…
We study some aspects of the representation theory of Mantaci-Reutenauer algebras: Cartan matrix, Loewy length, modular representations.
The projective representation of groups was introduced in 1904 by Issai Schur. It differs from the normal representation of groups by a twisting factor. It starts with a group T and a scalar valued function f on T^2 satisfying the…