In the mathematical field of representation theory, a highest-weight category is a k-linear category C (here k is a field) that * is locally artinian * has enough injectives * satisfiesfor all subobjects B and each family of subobjects {Aα} of each object X and such that there is a locally finite poset Λ (whose elements are called the weights of C) that satisfies the following conditions: * The poset Λ indexes an exhaustive set of non-isomorphic simple objects {S(λ)} in C. * Λ also indexes a collection of objects {A(λ)} of objects of C such that there exist embeddings S(λ) → A(λ) such that all composition factors S(μ) of A(λ)/S(λ) satisfy μ < λ. * For all μ, λ in Λ,is finite, and the multiplicityis also finite. * Each S(λ) has an injective envelope I(λ) in C equipped with an increasing filtrationsuch that 1. * 2. * for n > 1, for some μ = λ(n) > λ 3. * for each μ in Λ, λ(n) = μ for only finitely many n 4. * (Wikipedia).
This morning I set a one-rep-max personal record for the deadlift: 405 pounds, which is my first-ever lift over 400 pounds and ranks me at the 72nd percentile among male CrossFitters. This is a wide margin over previous PRs of 365 lb. (May 13th) and 315 lb. (December 2019).
From playlist Weightlifting
440-pound Deadlift: First Lift 2x Bodyweight
I weigh 220 pounds so this 440-pound deadlift is my first ever of twice my bodyweight and a new all-time PR. My previous PR was 405 pounds in May 2021; delighted to crush that figure a year later :)
From playlist Weightlifting
First Greater-than-Bodyweight Clean (225 pounds)
#olylifting #crossfit #fitness I weigh about 215 pounds, making this clean not only a personal record at 225 pounds, but also the first time I cleaned more than my bodyweight. Based on data from BeyondTheWhiteBoard, this lift is at the 64th percentile amongst male CrossFitters. Previo
From playlist Weightlifting
All-Time Snatch PR: 160 pounds
To hit this lift, I managed to persist through repeated failure immediately beforehand. After a gradual warm-up to 150#, I put 160# on the bar (a weight five pounds over my previous all-time PR, set nearly two years ago in March 2020). Then this happened: 1. Got 160# overhead but failed t
From playlist Weightlifting
More than Bodyweight Overhead for the First Time
#Weightlifting #OlyLift #CleanAndJerk This week, I power cleaned 220 pounds and then jerked it overhead! This is a big jump from the 205-pound clean-and-jerk personal record I set last month. It's also the first time I've either power cleaned or jerked more than my bodyweight (I weigh abo
From playlist Weightlifting
BRIAN SHAW'S WORLD RECORD 733 LB STONE LIFT | The Strongest Man in History | History
In Scotland, the strongmen attempt to lift and carry the legendary 733 lb. Dinnie Stones a record breaking 8'2" in this scene from Season 1, "Stronger Than a Scotsman". #StrongestMan Subscribe for more from Strongest Man in History and other great HISTORY shows: http://histv.co/SubscribeHi
From playlist Strongest Man In History | Official Series Playlist | History
EDDIE LIFTS A 3,500 POUND CAR 🚗 💪 | The Strongest Man in History | #Shorts
Eddie lifts a 3,500 pound Ford Mustang, in this clip from The Strongest Man in History. #StrongestMan Subscribe for more from Strongest Man in History and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryYT Watch more Strongest Man in History on YouTube in this pla
From playlist Strongest Man In History | Official Series Playlist | History
The Strongest Man in History: Barrel Lift Challenge (Season 1) | History
The guys take on a legendary three barrel lift challenge, which leads to an even greater competition between Nick Best and Brian Shaw in this clip from season 1, "One Ton Lift". #StrongestMan Subscribe for more from Strongest Man in History and other great HISTORY shows: http://histv.co/Su
From playlist Strongest Man In History: Season 1 | HISTORY
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 9
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Iva Halacheva: The cactus group, crystals, and perverse equivalences
Suppose C is a category equipped with a categorical action of a (simply-laced) semisimple Lie algebra g. Chuang and Rouquier construct equivalences on its derived category $D^b(C)$ via the so called Rickard complexes, one for each simple root of g. These complexes satisfy the braid relatio
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
2-Verma modules - Gregoire Naisse; Pedro Vaz
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: 2-Verma modules Speakers: Gregoire Naisse; Pedro Vaz Affiliation: University College London; University College London Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 20
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Introduction to quantized enveloping algebras - Leonardo Maltoni
Quantum Groups Seminar Topic: Introduction to quantized enveloping algebras Speaker: Leonardo Maltoni Affiliation: Sorbonne University Date: January 28, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Gwyn Bellamy: Graded algebras admitting a triangular decomposition
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The goal of this talk is to describe the representation theory of finite dimensional graded algebras A admitting a triangular decomposition (in much the s
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Why do we care about characters of tilting modules? - Shotaro Makisumi
SL2 Seminar Topic: Why do we care about characters of tilting modules? Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: January 26, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
The Strongest Man in History: Thor's Hammer Throw | Exclusive | History
Tune in to new episodes of "The Strongest Man in History" Wednesdays at 10/9c! The strongmen practice throwing a 13 pound hammer in this digital exclusive from "Stronger Than a Viking". #StrongestMan Subscribe for more from Strongest Man in History and other great HISTORY shows: http://hi
From playlist Strongest Man In History | Official Series Playlist | History
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 18
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
The Drinfeld-Sokolov reduction of admissible representations of affine Lie algebras - Gurbir Dhillon
Workshop on Representation Theory and Geometry Topic: The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras Speaker: Gurbir Dhillon Affiliation: Yale University Date: April 03, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
From playlist STAT 503