Representation theory of Lie groups | Harmonic analysis | Representation theory of groups
In mathematics, a Gelfand pair is a pair (G,K) consisting of a group G and a subgroup K (called an Euler subgroup of G) that satisfies a certain property on restricted representations. The theory of Gelfand pairs is closely related to the topic of spherical functions in the classical theory of special functions, and to the theory of Riemannian symmetric spaces in differential geometry. Broadly speaking, the theory exists to abstract from these theories their content in terms of harmonic analysis and representation theory. When G is a finite group the simplest definition is, roughly speaking, that the (K,K)-double cosets in G commute. More precisely, the Hecke algebra, the algebra of functions on G that are invariant under translation on either side by K, should be commutative for the convolution on G. In general, the definition of Gelfand pair is roughly that the restriction to K of any irreducible representation of G contains the trivial representation of K with multiplicity no more than 1. In each case one should specify the class of considered representations and the meaning of contains. (Wikipedia).
An excellent song which I could not find on Youtube.
From playlist the absolute best of stereolab
Stirring the Mandelbrot Set: a checkerboard
http://code.google.com/p/mandelstir/
From playlist mandelstir
This is the other case. The first one was rotation about yb and xa, or if you like x into a and y into b, this one is rotation about xb and ya or x into b and y into a. Now I have a strange feeling that there are again an inifinite number of mixed cases, but I will not think about that now
From playlist Fractal
Representations of Galois algebras – Vyacheslav Futorny – ICM2018
Lie Theory and Generalizations Invited Lecture 7.3 Representations of Galois algebras Vyacheslav Futorny Abstract: Galois algebras allow an effective study of their representations based on the invariant skew group structure. We will survey their theory including recent results on Gelfan
From playlist Lie Theory and Generalizations
Ben Webster: Gelfand-Tsetlin theory and Coulomb branches
Abstract: The algebra U(gln) contains a famous and beautiful commutative subalgebra, called the Gelfand-Tsetlin subalgebra. One problem which has attracted great attention over the recent decades is to classify the simple modules on which this subalgebra acts locally finitely (the Gelfand-
From playlist Algebra
Recollections of I.M. Gelfand [2013]
RECOLLECTIONS Thursday, August 29 3:30PM – 5:45PM Gelfand Recollections session (room 34-101; to be continued at the conference banquet) Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 http://math.mit.edu/conferences/Gelf
From playlist Mathematics
Hypergroup definition and five key examples | Diffusion Symmetry 4 | N J Wildberger
We state a precise definition of a finite commutative hypergroup, and then give five important classes of examples, 1) the class hypergroup of a finite (non-commutative) group G 2) the character hypergroup of a finite (non-commutative) group G 3) the hypergroup associated to a distance-tr
From playlist Diffusion Symmetry: A bridge between mathematics and physics
How to Create Order From Chaos, with Philippe Petit | Big Think
How to Create Order From Chaos, with Philippe Petit New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Working-class peop
From playlist Confessions of an Outlaw: A Creativity Workshop, with Philippe Petit
Conformal and DLR measures on Markov subshifts with infinitely many states – Ruy Exel – ICM2018
Analysis and Operator Algebras Invited Lecture 8.6 Conformal and DLR measures on Markov subshifts with infinitely many states Ruy Exel Abstract: We shall begin by briefly reviewing a compactification of the Markov space for an infinite transition matrix, introduced by Marcelo Laca and th
From playlist Analysis & Operator Algebras
From playlist the absolute best of stereolab
How power affects the way you behave—and the way you’re punished | Michele Gelfand | Big Think
How power affects the way you behave—and the way you’re punished Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Rules, whe
From playlist Best Videos | Big Think
What is the difference of a trapezoid and an isosceles trapezoid
👉 Learn how to solve problems with trapezoids. A trapezoid is a four-sided shape (quadrilateral) such that one pair of opposite sides are parallel. Some of the properties of trapezoids are: one pair of opposite sides are parallel, etc. A trapezoid is isosceles is one pair of opposite sides
From playlist Properties of Trapezoids
Linear Algebra Vignette 4b: Fibonacci Numbers As A Matrix Product
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Pierre Emmanuel Caprace - Groups with irreducibly unfaithful subsets for unitary representations
A subset F of a group G is called irreducibly faithful if G has an irreducible unitary representation whose kernel does not contain any non-trivial element of F. We say that G has property P(n) if every subset of size at most n is irreducibly faithful. By a classical result o
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Animated Mandelbrot transform - linear interpolation
http://code.google.com/p/mandelstir/
From playlist mandelstir
Markus Haase : Operators in ergodic theory - Lecture 1 : Operators dynamics versus ...
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 6
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi