Representation theory | Group theory

Character table

In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group elements. The entries consist of characters, the traces of the matrices representing group elements of the column's class in the given row's group representation. In chemistry, crystallography, and spectroscopy, character tables of point groups are used to classify e.g. molecular vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons. Many university level textbooks on physical chemistry, quantum chemistry, spectroscopy and inorganic chemistry devote a chapter to the use of symmetry group character tables. (Wikipedia).

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Character Tables for S4 and A4

Representation Theory of Finite Groups: We build the character tables for S4 and A4 from scratch. As an application, we use irreducible characters to decompose a tensor product.

From playlist Representation Theory

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Represent a Discrete Function Using Ordered Pairs, a Table, and Function Notation

This video explains how to represent a discrete function given as points as ordered pairs, a table, and using function notation. http://mathispower4u.com

From playlist Introduction to Functions: Function Basics

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A Simple Programming Language - (part 13 of 13)

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From playlist A Simple Programming Language

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Character Tables for S5 and A5

Representation Theory of Finite Groups: We compute the character tables of S5, the symmetric group on 5 letters, and A5, the subgroup of even permutations. We note that A5 is isomorphic to the group of rigid motions of an icosahedron.

From playlist Representation Theory

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Ex: Function Values of a Function of Two Variables Using a Table

This video provides an example of how to evaluate a function of two variables using a table of values. Site: http://mathispower4u.com

From playlist Functions of Several Variables

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Table Of Ordered Pairs: Substitution | Algebra | Maths | FuseSchool

In this video we’re going to look at how to use substitution in equations to generate a table of ordered pairs. Ordered pairs (coordinates) can be used to solve equations, to plot graphs, and so we come across them a lot in Maths. You should already know how to substitute into equations,

From playlist MATHS

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Application: ASCII! C tutorial 1.1

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From playlist C Tutorial

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Powers

"Understand power notation and calculate simple powers, e.g. squares, cubes."

From playlist Number: Powers, Roots & Laws of Indices

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Ex: Evaluate a Function and Solve for a Function Value Given a Table

The video explains how to determine a function value and solve for x given a function value when the function is given as a table. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Determining Function Values

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Chemistry 107. Inorganic Chemistry. Lecture 04

UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 04. Inorganic Chemistry -- Character Tables and One Application of Symmetry View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use:

From playlist Chem 107: Week 2

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Representation Theory(Repn Th) 1 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

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Representation Theory(Repn Th) 2 by Gerhard Hiss

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From playlist Group Theory and Computational Methods

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The S3 character table - a (somewhat) new meaning | Diffusion Symmetry 2 | N J Wildberger

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From playlist Diffusion Symmetry: A bridge between mathematics and physics

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New Local Properties in the Character Table by Gabriel Navarro

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From playlist Group Theory and Computational Methods

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!!Con 2018: Tales of ⌧! Can You Tell Your Story When Your Character Is Undefined?! by Persa Zula

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From playlist !!Con 2018

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Google Coding Interview Question and Answer #1: First Recurring Character

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From playlist Coding Interview Questions and Answers

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Molecular Structure & Statistical Mechanics 131B. Lecture 03. Transformation Matrices.

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CS105: Introduction to Computers | 2021 | Lecture 1.4 BB&B: Represent Hieroglyphs on a Computer

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From playlist Stanford CS105 - Introduction to Computers Full Course

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Representation theory: Orthogonality relations

This lecture is about the orthogonality relations of the character table of complex representations of a finite group. We show that these representations are unitary and deduce that they are all sums of irreducible representations. We then prove Schur's lemma describing the dimension of t

From playlist Representation theory

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Representation theory: Introduction

This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr

From playlist Representation theory

Related pages

Elementary abelian group | Modular representation theory | Character theory | DFT matrix | Character group | Tensor product | Crystallography | Trace (linear algebra) | Kernel (linear algebra) | Fourier analysis | Up to | Group (mathematics) | Class function | Identity element | Group isomorphism | Trivial representation | Finite group | Representation theory of finite groups | Dihedral group | Group theory | Conjugacy class | Molecular symmetry | List of character tables for chemically important 3D point groups | Regular representation | Abstract algebra | Commutator subgroup | Irreducible representation | Inner automorphism | Quaternion group