Representation theory

Trivial representation

In the mathematical field of representation theory, a trivial representation is a representation (V, φ) of a group G on which all elements of G act as the identity mapping of V. A trivial representation of an associative or Lie algebra is a (Lie) algebra representation for which all elements of the algebra act as the zero linear map (endomorphism) which sends every element of V to the zero vector. For any group or Lie algebra, an irreducible trivial representation always exists over any field, and is one-dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebras and unital representations. Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors; so that searching for such subrepresentations is the whole topic of invariant theory. The trivial character is the character that takes the value of one for all group elements. (Wikipedia).

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Simplifying a rational expression by factoring

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

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Solve an equation with a rational term

πŸ‘‰ Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

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Math tutorial for solving rational equations

πŸ‘‰ Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

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Learn how to solve a rational expression by multiplying by the LCD

πŸ‘‰ Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

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How to solve a rational equation

πŸ‘‰ Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

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What are rational expressions

πŸ‘‰ Learn about solving rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual ration

From playlist How to Solve Rational Equations | Learn About

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Solving a rational Equation

πŸ‘‰ Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual rationa

From playlist How to Solve Rational Equations with an Integer

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Yanli Song: K-theory of the reduced C*-algebra of a real reductive Lie group

Talk by Yanli Song in Global Noncommutative Geometry Seminar (Americas) on January 28, 2022 in https://globalncgseminar.org/talks/tba-23/

From playlist Global Noncommutative Geometry Seminar (Americas)

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Introductory courses on Arthur packets 2

Wee Teck Gan National University of Singapore, Singapore Hiraku Atobe Hokkaido University, Japan

From playlist Introduction courses to Arthur packets

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How to solve an equation with an expression raised to a fractional power

πŸ‘‰ Learn how to deal with Rational Powers or Exponents. Exponents are shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power", where the exponent is the "power". Rational exponents are exponents that are fractions. To

From playlist Solve Equations with Fractional Exponents

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Moduli Stacks of Galois Representations by Mathew Emerton

Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou

From playlist Recent Developments Around P-adic Modular Forms (Online)

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Dipendra Prasad - Branching laws: homological aspects

By this time in the summer school, the audience will have seen the question about decomposing a representation of a group when restricted to a subgroup which is referred to as the branching law. In this lecture, we focus attention on homological aspects of the branching law. The lecture

From playlist 2022 Summer School on the Langlands program

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Omer Offen : Distinction and the geometric lemma

Recording during the thematic Jean-Morlet Chair - Doctoral school: "Introduction to relative aspects in representation theory, Langlands functoriality and automorphic forms" the May 17, 2016 at the Centre International de Rencontres MathΓ©matiques (Marseille, France) Filmmaker: Guillaume H

From playlist Jean-Morlet Chair - Research Talks - Prasad/Heiermann

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How to solve an equation with fraction powers in your exponent

πŸ‘‰ Learn how to deal with Rational Powers or Exponents. Exponents are shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power", where the exponent is the "power". Rational exponents are exponents that are fractions. To

From playlist Solve Equations with Fractional Exponents

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Kevin Buzzard (lecture 16/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

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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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Representation theory: Examples D8, A4, S4, S5, A5

In this talk we calculate the character tables of several small groups: the dihedral group of order 8, and the alternating and symmetric groups on 4 and 5 points. We do this by first finding the 1-dimensional characters, then finding a few other characters by looking at permutation repres

From playlist Representation theory

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Symmetry indicators of topological superconductors by Haruki Watanabe

DISCUSSION MEETING NOVEL PHASES OF QUANTUM MATTER ORGANIZERS: Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara DATE: 23 December 2019 to 02 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Recent theoretical and experimental

From playlist Novel Phases of Quantum Matter 2019

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Summary for solving rational equations

πŸ‘‰ Learn about solving rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of the ways is by multiplying all the individual ration

From playlist How to Solve Rational Equations | Learn About

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Eisenstein series, p-adic deformations, Galois representations, and the group G_2 - Sam Mundy

Joint IAS/Princeton University Number Theory Seminar Topic: Eisenstein series, p-adic deformations, Galois representations, and the group G_2 Speaker: Sam Mundy Affiliation: Columbia University Date: April 01, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Related pages

Algebra representation | Linear map | Group representation | Unital algebra | Character (mathematics) | Invariant theory | Lie algebra | Mathematics | Field (mathematics) | Associative algebra | Lie algebra representation | Irreducible representation | Endomorphism | Representation (mathematics) | Group (mathematics) | Representation theory