Representation theory

Subrepresentation

In representation theory, a subrepresentation of a representation of a group G is a representation such that W is a vector subspace of V and . A finite-dimensional representation always contains a nonzero subrepresentation that is irreducible, the fact seen by induction on dimension. This fact is generally false for infinite-dimensional representations. If is a representation of G, then there is the trivial subrepresentation: (Wikipedia).

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Intro to Subsequences | Real Analysis

What are subsequences in real analysis? In today's lesson we'll define subsequences, and see examples and nonexamples of subsequences. We can learn a lot about a sequence by studying its subsequence, so let's talk about it! If (a_n) is a sequence, we can denote a subsequence of (a_n) as (

From playlist Real Analysis

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Andrew Putman - The Steinberg representation is irreducible

The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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RT6. Representations on Function Spaces

Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in

From playlist Representation Theory

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Lie groups: Haar measure

This lecture is part of an online graduate course on Lie groups. We show the existence of a left-invariant measure (Haar measure) on a Lie group. and work out several explicit examples of it. Correction: At 21:40 There is an exponent of -1 missing: the parametrization of the unitary gro

From playlist Lie groups

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Giovanni Cerulli-Irelli : Quiver Grassmannians of Dynkin type

Abstract: Given a finite-dimensional representation M of a Dynkin quiver Q (which is the orientation of a simply-laced Dynkin diagram) we attach to it the variety of its subrepresentations. This variety is strati ed according to the possible dimension vectors of the subresentations of M. E

From playlist Algebra

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Alexander Petrov - Automatic de Rhamness of p-adic local systems and Galois action on the (...)

Given a $p$-adic local system $L$ on a smooth algebraic variety $X$ over a finite extension $K$ of $Q_p$, it is always possible to find a de Rham local system $M$ on $X$ such that the underlying local system $L|_{X_{\overline{K}}}$ embeds into $M|_{X_{\overline{K}}}$. I will outline the pr

From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)

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My MSc Defense: Part Two

In this video I *briefly* go over what it means to be a highest weight vector, and outline the strategy of my proof. Intro (0:00) Highest Weight Vectors (1:47) Plan of Attack (10:10)

From playlist Unitary Schwartz forms & the Weil Representation

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Fraction misconception adding the numerator and the denominator

👉 Learn how to add or subtract fractions with common denominators. When adding or subtracting two or more fractions with common denominators, we add or subtract only the numerator while we keep the denominator the same. We will then simplify our answer by reducing the fraction if necessar

From playlist Add and Subtract Fractions with Like Denominators

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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

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Subtracting polynomials by using the addition method

👉 Learn how to subtract polynomials. To subtract polynomials, we first simplify the polynomials by removing all brackets. Then, we combine like terms. Like terms are terms that share the same base and power for each variable. When you have identified the like terms, we then apply the requ

From playlist How to subtract polynomials

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 02 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

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01b Spatial Data Analytics: Subsurface Data

Lecture of the data available for subsurface modeling.

From playlist Spatial Data Analytics and Modeling

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 12 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 10 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 18 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 16 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 5

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Henniart: Classification des représentations admissibles irréductibles modulo p...

Recording during the thematicmeeting : "Algebraic and Finite Groups, Geometry and Representations. Celebrating 50 Years of the Chevalley Seminar " the September 23, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this

From playlist Partial Differential Equations

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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 17 | #cybersecurity

Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

From playlist Comprehensive Subdomain Enumeration

Related pages

Group representation | Irreducible representation | Mathematical induction | Group (mathematics) | Representation theory