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
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
Representation Theory as Gauge Theory - David Ben-Zvi [2016]
Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G
From playlist Number Theory
Representation theory: Induced representations
We define induced representations of finite groups in two ways as either left or right adjoints of the restriction functor. We calculate the character of an induced representation, and give an example of an induced representation of S3.
From playlist Representation theory
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***
Representation Theory: We explain unitarity and invariant inner products for representations of finite groups. Full reducibility of such representations is derived. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/UR-RepTheory.html
From playlist Representation Theory
Representation theory: Abelian groups
This lecture discusses the complex representations of finite abelian groups. We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality). We check the orthogonality relations for the
From playlist Representation theory
PiTP-Supersymmetric Grand Unification, Part 1 - Stuart Raby
PiTP-Supersymmetric Grand Unification, Part 1 Stuart Raby The Ohio State University July 14, 2008
From playlist PiTP 2008
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
SQCD and Pairs of Pants by Shlomo Razamat
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
A Mathematical Introduction to 3d N = 4 Gauge Theories (Lecture 1) by Mathew Bullimore
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
PiTP-Supersymmetric Grand Unification, Part 2 - Stuart Raby
PiTP-Supersymmetric Grand Unification, Part 2 Stuart Raby The Ohio State University July 17, 2008
From playlist PiTP 2008
An Introduction to Class-S and Tinkertoys (Lecture 2 )by Jacques Distler
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Lecture 4 | New Revolutions in Particle Physics: Standard Model
(February 1, 2010) Professor Leonard Susskind continues his discussion of group theory. This course is a continuation of the Fall quarter on particle physics. The material will focus on the Standard Model of particle physics, especially quantum chromodynamics (the theory of quarks) and th
From playlist Lecture Collection | Particle Physics: Standard Model
Supersymmetric gauge theories (Lecture 4) by Shiraz Minwalla
Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018 DATE:08 January 2018 to 18 January 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology is a pan-Asian collaborative effort of high energy theori
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - M.Brannan
Michael Brannan (College station) / 12.09.17 Title: Entangled subspaces from quantum groups and their associated quantum channels. Abstract:I will describe a class of highly entangled subspaces of bipartite quantum systems arising from the representation theory of a class of compact quan
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
A simple Qubit Regularization Scheme for SU(N) Lattice Gauge Theories by Shailesh Chandrasekharan
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
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
Wall Crossing, Part 1 - Greg Moore
Wall Crossing, Part 1 Greg Moore Rutgers, The State University of New Jersey July 27, 2010
From playlist PiTP 2010