Mathematics - Representation Theory

CombinatoricsNew Insights in Combinatorial Theory: The Macdonald Piece Polynomial

Exploring the Macdonald piece polynomial and its connections to combinatorial conjectures.

Donghyun Kim, Jaeseong Oh

2025-06-13T12:51:08+00:00 ― 5 min read

Representation TheoryThe Significance of Weight Multiplicities in Mathematics

This article explores weight multiplicities and their connections in algebra and representation theory.

Seung Jin Lee

2025-06-13T03:14:22+00:00 ― 5 min read

Representation TheoryExploring the Depths of Lie Superalgebras

A study of Lie superalgebras and their significance in mathematics and physics.

Sidarth Erat, Arun S. Kannan, Shihan Kanungo

2025-06-12T02:46:14+00:00 ― 5 min read

ProbabilityThe Impact of Random Unitary Matrices

Examining random unitary matrices and their implications in representation theory.

Michael Magee, Mikael de la Salle

2025-06-11T16:17:02+00:00 ― 5 min read

Quantum AlgebraVertex Operator Algebras: Bridging Math and Physics

Explore the role of vertex operator algebras in mathematics and physics.

Cuipo Jiang, Jingtian Song

2025-06-11T14:58:23+00:00 ― 4 min read

Analysis of PDEsSemiclassical Functional Calculus on Nilpotent Lie Groups

Research on operators in nilpotent Lie groups reveals new insights in harmonic analysis.

Véronique Fischer, Søren Mikkelsen

2025-06-11T08:37:12+00:00 ― 4 min read

Algebraic GeometryInterconnections in Quantum Field Theories

Exploring the relationships between quantum field theories and mathematical frameworks.

Hiraku Nakajima

2025-06-10T15:44:33+00:00 ― 6 min read

Algebraic GeometryAn Overview of Schubert and Spherical Varieties

Learn about important types of varieties in algebraic geometry.

Mahir Bilen Can, S. Senthamarai Kannan, Pinakinath Saha

2025-06-10T14:56:28+00:00 ― 4 min read

Representation TheoryRigidity of Simple Modules in Algebraic Groups

This article reviews the rigidity properties of simple modules within algebraic groups.

Michael Bate, David I. Stewart

2025-06-10T07:30:47+00:00 ― 4 min read

Symplectic GeometryConnecting Local and Global Properties in Geometry

Research on Legendrian links and Lagrangian fillings reveals important geometric relationships.

Roger Casals, Wenyuan Li

2025-06-09T01:48:03+00:00 ― 4 min read

Representation TheoryUnderstanding Macdonald Identities in Mathematics

An overview of Macdonald identities and their significance in root systems.

K. Iohara, Y. Saito

2025-06-09T00:55:37+00:00 ― 3 min read

Representation TheoryInsights into Higher Spin Representations and Kac-Moody Algebras

This article discusses higher spin representations in Kac-Moody algebras and their significance.

Robin Lautenbacher, Ralf Köhl

2025-06-09T00:03:11+00:00 ― 6 min read

Representation TheoryGentle and Locally Gentle Algebras: An Overview

A look into gentle and locally gentle algebras and their properties.

S. Ford, A. Oswald, J. J. Zhang

2025-06-08T13:07:46+00:00 ― 6 min read

Representation TheoryAn Overview of Lie Algebras and Kac Diagrams

Learn about Lie algebras, Cartan subalgebras, and their relationships through Kac diagrams.

Stephen DeBacker, Jacob Haley

2025-06-08T03:57:13+00:00 ― 4 min read

Representation TheoryUnderstanding Terwilliger Algebras and Association Schemes

A look into Terwilliger algebras and their role in association schemes.

Nicholas L. Bastian, Stephen P. Humphries

2025-06-08T03:04:47+00:00 ― 5 min read

Representation TheoryInvestigating Camina Groups and Terwilliger Algebras

A detailed exploration of Camina groups and their algebraic properties.

Nicholas L. Bastian

2025-06-07T09:36:07+00:00 ― 5 min read

Number TheoryUnderstanding Symmetric Functions and Their Applications

An overview of symmetric functions, their properties, and key applications in mathematics.

Milo Bechtloff Weising

2025-06-07T00:51:47+00:00 ― 7 min read

Algebraic GeometrySimplifying Key Concepts in Algebraic Geometry

A look into varieties, stratifications, and monomial theories explained simply.

Henrik Müller

2025-06-06T00:49:52+00:00 ― 3 min read

Representation TheoryKey Insights into Diagram Algebras and Local Noetherianity

Exploring the structure and significance of diagram algebras in mathematics.

Anthony Muljat, Khoa Ta

2025-06-05T19:35:16+00:00 ― 4 min read

Quantum AlgebraCommutative Algebras and Their Role in Mathematics

An overview of commutative algebras and their applications in advanced mathematical contexts.

Thomas Creutzig, Robert McRae, Kenichi Shimizu

2025-06-05T03:59:36+00:00 ― 5 min read

Machine LearningAnalyzing Neural Networks with Quiver Representation Theory

A new method enhances understanding and reliability of neural networks.

Samuel Leblanc, Aiky Rasolomanana, Marco Armenta

2025-06-04T17:48:29+00:00 ― 5 min read

Algebraic GeometryQuantum Theory and Flag Varieties: A New Perspective

Research reveals connections between quantum theory and mathematical structures.

Irit Huq-Kuruvilla

2025-06-04T14:54:36+00:00 ― 4 min read

Representation TheoryRoot Systems: Structural Constants and Their Applications

An overview of root systems and their role in mathematics and beyond.

Rafael Stekolshchik

2025-06-04T11:41:27+00:00 ― 4 min read

Algebraic TopologyConnecting Persistence Diagrams and Schubert Calculus

This article explores the intersection of persistence diagrams and Schubert calculus for better data analysis.

Yasuaki Hiraoka, Kohei Yahiro, Chenguang Xu

2025-06-04T09:04:09+00:00 ― 5 min read

CombinatoricsUnderstanding Scattering Diagrams and Gradings in Mathematics

A clear guide to scattering diagrams, gradings, and positivity in combinatorics.

Amanda Burcroff, Kyungyong Lee, Lang Mou

2025-06-03T11:13:19+00:00 ― 7 min read

Number TheoryOperators, Functions, and Number Theory: A Deep Dive

Explore the connections between operators, functions, and number theory.

Zhilin Luo, Ngo Bao Chau

2025-06-03T00:17:54+00:00 ― 5 min read

CombinatoricsStable Class Functions in Linear Groups

Exploring stable class functions and their applications in representation theory and beyond.

Danielle Ernst-West, Doron Puder, Yotam Shomroni

2025-06-02T16:26:00+00:00 ― 5 min read

Representation TheoryUnderstanding Highest Weight Modules in Representation Theory

An overview of highest weight modules, their properties, and significance in representation theory.

Zhanqiang Bai, Markus Hunziker

2025-06-02T15:33:34+00:00 ― 6 min read

Number TheoryThe Interplay of Modular Forms and Quadratic Fields

Examining how modular forms relate to quadratic fields through periods and zeta functions.

Alexandros Groutides

2025-06-01T08:05:58+00:00 ― 5 min read

Rings and AlgebrasGraded Identities: A Simple Approach to Complexity

Learn how graded identities simplify mathematical structures by organizing elements into groups.

Cássia F. Sampaio, Plamen E. Koshlukov

2025-05-29T20:21:07+00:00 ― 7 min read

Representation TheoryConnecting Algebra and Graph Theory

Discover the links between bipartite graphs and algebra in a friendly way.

Karin M. Jacobsen, Mads Hustad Sandøy, Laertis Vaso

2025-05-28T16:56:21+00:00 ― 6 min read

Representation TheoryUnderstanding the FPP Conjecture

A look into the FPP conjecture and its significance in mathematics.

Dougal Davis, Lucas Mason-Brown

2025-05-28T09:00:14+00:00 ― 6 min read

Representation TheoryUnderstanding Exceptional Groups and Their Significance

A look at exceptional groups and their role in mathematics.

Marcela Hanzer, Gordan Savin

2025-05-28T06:07:06+00:00 ― 6 min read

CombinatoricsMachine Learning and Mutation-Acyclic Quivers

Using machine learning to study mutation-acyclic quivers with four points.

Kymani T. K. Armstrong-Williams, Edward Hirst, Blake Jackson

2025-05-27T04:47:45+00:00 ― 6 min read

Representation TheoryThe Cayley Transform: A Key Tool in Mathematics

Explore the significance of the Cayley transform in Lie group representations.

Jingyu Lu, Ke Ye

2025-05-26T20:12:47+00:00 ― 5 min read

Representation TheoryThe Harmony of Two Mathematical Languages

Exploring the relationship between Kazhdan-Lusztig and Gelfand-Tsetlin bases.

Ali Haidar, Oded Yacobi

2025-05-25T14:38:10+00:00 ― 5 min read

Representation TheoryAn Introduction to String Almost Gentle Algebras

Explore the unique features of string almost gentle algebras and their connections.

Yu-Zhe Liu, Panyue Zhou

2025-05-24T23:29:13+00:00 ― 5 min read

Algebraic GeometryThe Intriguing World of Twisted Bundles

Discover the balance between stability and wobbliness in twisted bundles.

Kuntal Banerjee, Steven Rayan

2025-05-23T01:19:05+00:00 ― 7 min read

Numerical AnalysisSimplifying Partial Differential Equations with Symmetry

Learn how symmetry helps in simplifying complex PDEs effectively.

Sheehan Olver

2025-05-21T02:25:40+00:00 ― 8 min read

Representation TheoryConnections Between Weyl Modules and Homomorphisms

Exploring relationships and characteristics of Weyl modules and homomorphisms.

Charalampos Evangelou

2025-05-20T19:56:07+00:00 ― 6 min read