Lemmas | Representation theory
In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0. An important special case occurs when M = N, i.e. φ is a self-map; in particular, any element of the center of a group must act as a scalar operator (a scalar multiple of the identity) on M. The lemma is named after Issai Schur who used it to prove the Schur orthogonality relations and develop the basics of the representation theory of finite groups. Schur's lemma admits generalisations to Lie groups and Lie algebras, the most common of which are due to Jacques Dixmier and Daniel Quillen. (Wikipedia).
Physics - Chapt. 66 Quantum Mechanics (8 of 9) Schrodinger's Equation
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce Schrodinger and explain his partial differential equation describing how the quantum state changes with time. Next video in the series can be seen at: https://youtu.be/lptfhi_cQLc
From playlist PHYSICS 66 - QUANTUM MECHANICS
RT4.2. Schur's Lemma (Expanded)
Representation Theory: We introduce Schur's Lemma for irreducible representations and apply it to our previous constructions. In particular, we identify Hom(V,V) with invariant sesquilinear forms on V when (pi, V) is unitary. Course materials, including problem sets and solutions, availa
From playlist Representation Theory
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (13 of 92) Time & Position Dependencies 2/3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find C=?, of the position part of the Schrodinger's equation by using the time dependent part of Schrodinger's equation, part 2/3. Next video in this series can be seen at: https://youtu.be/1mxipWt-W
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Physicist Explains Wikipedia Page: The Schrodinger Equation
Why are Wikipedia Physics pages so difficult to understand? Hey guys, I'm back with a new video! This time, I'm looking at how certain Wikipedia pages can be so complicated to understand, and so here's a Wikipedia page made easy! Now I can totally understand that a wiki page is meant to p
From playlist Quantum Physics by Parth G
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Representation theory: The Schur indicator
This is about the Schur indicator of a complex representation. It can be used to check whether an irreducible representation has in invariant bilinear form, and if so whether the form is symmetric or antisymmetric. As examples we check which representations of the dihedral group D8, the
From playlist Representation theory
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
RT8.1. Schur Orthogonality Relations
Representation Theory of Finite Groups: As a first step to Fourier analysis on finite groups, we state and prove the Schur Orthogonality Relations. With these relations, we may form an orthonormal basis of matrix coefficients for L^(G), the set of functions on G. We also define charac
From playlist *** The Good Stuff ***
Math 060 Fall 2017 112917C Spectral Theorem for Hermitian Matrices
Review: A Hermitian matrix with all distinct eigenvalues is unitarily diagonalizable. Statement of Spectral Theorem: Every Hernitian matrix is unitarily diagonalizable. Lemma: Schur's Theorem (every matrix is unitarily upper triangularizable). Inductive proof of Schur's theorem. Proof
From playlist Course 4: Linear Algebra (Fall 2017)
RT5. Mostly Exercises (Expanded)
Representation Theory: We collect some loose ends and noteworthy facts on representations as a set of exercises. Topics include Schur's Lemma, full reducibility, and tensor product representations. Course materials, including problem sets and solutions, available at http://mathdoctorbob
From playlist Representation Theory
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
How to use Group Theory in Physics ?
Group theory in Physics, an introduction (#SoME1) Timestamps: 0:00 - Introduction 0:30 - Defining the problem 1:04 - Equation we want to solve 2:44 - Symmetries of the molecule 6:06 - What is a Group ? 7:31 - What is a Representation ? 9:24 - What is a reducible Representation ? 12:52 - D
From playlist Summer of Math Exposition Youtube Videos
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (12 of 92) Time & Position Dependencies 1/3
Visit http://ilectureonline.com for more math and science lectures! In this video I will separate the time and position dependencies of the Schrodinger's equation, part 1/3. Next video in this series can be seen at: https://youtu.be/djlpmDUtIZY
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (4 of 92) The Schrodinger Eqn. "Derived"
Visit http://ilectureonline.com for more math and science lectures! In this video I will “derive” the Schrodinger equation using y(x,y)=Acos(kx-wt). Next video in this series can be seen at: https://youtu.be/GyKk2-0JZ48
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (1 of 92) The Wave Equation
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the Schrodinger equation used to describe the properties of motion, energy, and positions of small particles behaving more like photons than “real” particles. Next video in this series can be
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Representation of finite groups over arbitrary fields by Ravindra S. Kulkarni
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
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
RT7.1: Finite Abelian Groups: Character Orthogonality
We establish an analogue of Fourier analysis for a finite abelian group G. A decomposition of L^2(G) is given in terms of characters. Versions of Schur Orthogonality Relations and the Peter-Weyl Theorem are given. Course materials, including problem sets and solutions, available at htt
From playlist Representation Theory
1. A bridge between graph theory and additive combinatorics
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In an unsuccessful attempt to prove Fermat's last theorem
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Dealing with Schrodinger's Equation - The Hamiltonian
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Schrodinger's
From playlist Quantum Mechanics