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: 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
Representations of Finite Groups | Definitions and simple examples.
We define the notion of a representation of a group on a finite dimensional complex vector space. We also explore one and two dimensional representations of the cyclic group Zn. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.mich
From playlist Representations of Finite Groups
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 ***
RT4.1. Constructions from Linear Algebra (Expanded)
Representation Theory: We apply techniques from linear algebra to construct new representations from old ones. Constructions include direct sums, dual spaces, tensor products, and Hom spaces. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/U
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: 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
Representations of Finite Groups | A few more common examples.
We present a few more common examples of representations of finite groups. These include cyclic groups, dihedral groups, the quaternions, and the symmetric group. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net R
From playlist Representations of Finite Groups
[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS
Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou
From playlist BOURBAKI - 2018
Lucas Mason-Brown - Arthur's Conjectures and the Orbit Method for Real Reductive Groups
The most fundamental unsolved problem in the representation theory of Lie groups is the Problem of the Unitary Dual: given a reductive Lie group G, this problem asks for a parameterization of the set of irreducible unitary G-representations. There are two big "philosophies" for approaching
From playlist 2022 Summer School on the Langlands program
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
Marko Tadic - Unitarizability in generalised rank three case for classical p-adic groups
J. Arthur has classified irreducible tempered representations of classical p-adic groups. C. Moeglin has singled out parameters of cuspidal representations among them. Further, she gave a simple formula forcuspidal reducibilities (in the generalised rank one). In our talk, we sh
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
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 ***
The local Gan-Gross-Prasad conjecture for real unitary groups - Hang Xue
Joint IAS/Princeton University Number Theory Seminar Topic: The local Gan-Gross-Prasad conjecture for real unitary groups Speaker: Hang Xue Affiliation: The University of Arizona Date: March 25, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory
Cohomological Automorphic Representations on Unitary Groups - Rahul Dalal
Joint IAS/PU Number Theory Seminar Topic: Applications of the Endoscopic Classification to Statistics of Cohomological Automorphic Representations on Unitary Groups Speaker: Rahul Dalal Affiliation: Johns Hopkins University Date: November 03, 2022 Consider the family of automorphic repre
From playlist Mathematics
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)
Alexey Bufetov: Representations of classical Lie groups: two growth regimes
Asymptotic representation theory deals with representations of groups of growing size. For classical Lie groups there are two distinguished regimes of growth. One of them is related to representations of infinite-dimensional groups, and the other appears in combinatorial and probabilistic
From playlist Probability and Statistics
This video discusses unitary matrix transformations and how they relate to the geometry of the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: h
From playlist Data-Driven Science and Engineering