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Swaggy Bro Sidney Crosby Was At The Justin Bieber Concert Last NightS |
Seriously, we have no idea why he was there (Tyler Kennedy too, apparently). It just started as a Twitter rumor that Crosby was in the house, but photographic evidence has emerged. Maybe he likes it? Maybe he chaperoned his 16-year-old sister? Maybe Mario Lemieux finally kicked him out of the house and now Crosby just ... |
Without the lockout, the Penguins would have played in Detroit Monday night and be preparing to host the Devils tonight. Aren't you glad we're getting Justin Bieber concert attendance news instead of that? |
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Let $G$ be a connected complex semisimple Lie-group, $T$ a maximal torus and $B$ a Borel subgroup containing it. Let $\phi:G\rightarrow G/B$ denote the projection. Given a representation ($\theta,V$) of $B$, we can define a $G$-equivariant holomorphic vector bundle over the flag variety $X:=G/B$ by $$ G\times_B V :=(G\... |
An integral weight $\lambda$ of $T$ gives a character $\chi_\lambda$ of $B$. Let $\theta\otimes\chi_\lambda$ denote the tensor product of the representations $\theta$ and $\chi_\lambda$. Suppose ($\theta,V$) is the restriction of a representation ($\pi,V$) of $G$, then the associated ($G$-equivariant) vector bundle is ... |
I have been reading about the Borel-Weil theorem lately, and |
Edit: This question arose from an attempt to fix a mistake in a book. The identity is indeed correct and I believe I have found the error elsewhere. Thanks Chuck and Jim! |
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I don't think that's correct; you should have $V$ instead of $V^*$ in the identity. For example, consider the trivial $G$-equivariant bundle on $G/B$ with fiber $V$; its global sections are isomorphic to $V$. – Chuck Hague Sep 4 '10 at 15:00 |
Silly nitpick: In the second line, $\phi$ should map to $X$, not $B$. – S. Carnahan Sep 5 '10 at 9:46 |
@Scott: Edited. – Jim Humphreys Sep 10 '10 at 22:36 |
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1 Answer |
up vote 2 down vote accepted |
This may be too naive an answer, but from my experience this kind of question fits comfortably into the foundational material for reductive algebraic groups over an algebraically closed field of arbitrary characteristic. This is for example treated in Part I of J.C. Jantzen's 2003 AMS second edition of Representations ... |
Most of what goes into the classical Borel-Weil theory has a natural formulation in any characteristic, though Bott's theorem can't be imitated so precisely for nondominant line bundles. |
P.S. There are quite a few literature sources (papers by H.H. Andersen, Cline-Parshall-Scott, Donkin, etc.), but Chapter II.5 in Jantzen's book gives a fairly comprehensive treatment in algebraic language of the theorems of Borel-Weil and Bott, along with a derivation of Weyl's character formula. To get back to the cla... |
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Brothers (photo: Getty Images)A new study indicates that first-born children perform better in school and also suggests why. It's not that they are smarter or have higher self-esteem, but that their parents are tougher on them. "People shouldn't feel limited because they are the second or third child," V. Joseph Host o... |
More on Yahoo: Parents Feel Weighed Down by Kids' Homework Burden |
The authors, who are both economists, looked at data from the National Longitudinal Survey of Youth, which surveyed more than 12,000 participants. The study controlled gender, divorce, family size, and other factors that might have influenced the outcomes. They found that parents of earlier-born children were harder on... |
Susan Whitbourne, a professor of psychology at the University of Massachusetts, says she appreciates the study's approach because it's focusing on the role of the parent rather than something intrinsic to a child. "There is so much that's written on birth order that seems very deterministic," she tells Yahoo Shine. "Th... |
More on Yahoo: Kelly Clarkson Has Lullabies and Homework on the Brain |
The fascination with birth order and its effect on personality and success goes back more than 100 years, when Austrian psychologist Alfred Adler, a contemporary of Sigmund Freud, first theorized that birth order has an inherent role in shaping personality and classified characteristics of first-, second-, and last-bor... |
More on Yahoo Shine: 7 Teacher-Approved Tips to Help Kids Be Better Students |
Since Adler's era, there have been more than 1,000 scholarly articles and many books published on the topic. The result of such intense interest is that today, the idea of birth-order-influenced traits has become codified – almost like one's zodiac sign. At the same time, because people believe so strongly in the signi... |
A 2012 review looked at 200 studies on the topic and found that certain themes did emerge in defining the characteristics of people depending on when they were born. According to their tabulation of the data: |
First-born children are often highly motivated, Type A personalities who are vulnerable to stress. They are the most conformist and influenced by authority. |
Middle children are sociable and least prone to "acting out." They can also exhibit feelings of being an outsider. |
Youngest children show the highest degree of sociability and empathy. They are also the most rebellious. |
Only children have a strong need to achieve, are intelligent, and exhibit the most behavioral problems. |
But, Whitbourne stresses that birth order is not destiny. She encourages parents to look at their own biases and nurture each of their individual children's strengths. That might mean letting your eldest child's grades slide on occasion and telling your youngest to turn off the TV and hit the books. |
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On the line: With a tentative settlement in the two-week-long UPS strike reached on Monday, the AFL-CIO claimed "a major victory for working people" in its first major contract negotiations under new leadership. |
Big labor is putting the move back in the labor movement |
By Todd Gitlin |
THURSDAY NIGHT and Friday, Oct. 3 and 4, something rarer than a picture of Dick Morris on the cover of Time magazine is going to happen in New York. Two endangered species are going to see what they can do for each other. Intellectuals of the left, in cahoots with the AFL-CIO leadership, summon one and all to gather at... |
It's been less than a year since American labor decided to take the cure, with, of all things, a contested election. It took the AFL-CIO longer than the erstwhile Communist regimes of the Soviet empire--culminating in the ascendancy of John Sweeney, the reformers' hope. Sweeney and his team are not just talking the tal... |
Under the rubric of Union Summer, with intended echoes of Mississippi 1964, some 1,000 young people, including a contingent of Santa Rosa Junior College students, took the summer off to set up at factories and offices, doing the hard work of campaigning to make it possible for unions to compete in fair elections. They ... |
This is the kind of lesson that lasts a lifetime. A career as union organizer might just turn out to be the sort that grows as fast as that of security guard. |
Turning the AFL-CIO around, even with a new captain, is like turning a supertanker around. This isn't the first time the AFL-CIO has talked the talk. As NYU journalism chairman William Serrin reminds us, 50 years ago the CIO put together Operation Dixie to organize Southern workers, and in 1955, the merged labor federa... |
The unions are pushing upstream, which is not impossible but requires a lot of muscle. They are up against global corporations that can blithely reassign production anyplace on the planet. They face outsourcing and downsizing, global competition, steadily fancier machines, and an unfriendly government. |
The last is one area where the unions could use public support. They have taken a bath in the public bassinet. Less than 20 years ago, in 1977, almost one quarter of American workers belonged to unions. Today it is only 1 in 6--only 1 in 9 in the private sector. While some would argue that unions are so lean because th... |
Despite occasional moves, such as, most recently, the minimum wage boost, Bill Clinton, who governed one of the decidedly less unionized states in the country, has never had much time for labor. If there is any union background in his family, he has shut up about it. We know more about his underwear. |
Even if it's not immense, labor has at least begun to draw blood as a stand-up bogeyman for the right. As the AFL-CIO started early, pouring unprecedented sums into congressional races at the start of the year, Republicans went gangbusters with their rhetoric machine. With indignant yelps from the likes of Trent Lott a... |
But labor needs more than to cry foul against pro-business media and politics. It needs to tend to both horns of the dilemma: to stake out big purposes and to win more fights. |
When I mentioned this week's teach-in to a friend of mine, a lifelong partisan of labor, he said, "You know why this is happening now? Labor has fallen so far that students can finally see it as a victim group." A crack as hopeful as it is cynical, actually, and he has a point. The left-of-center politics of the middle... |
Downsized professionals, students, and intellectuals may be coming to understand that the exotic others are themselves, or their cousins and aunts. The biggest unions now include teachers and clericals--and, significantly, large proportions of women and people of color. Unions are, in crucial fact, the major transracia... |
Those who wearily stare at the limits of identity politics have sorely needed a cross-category federation, an actually existing movement, in which people of various types work together because their common condition matters more than their differences. |
Decades have passed since labor was a cause among the chattering classes. In the fabled '30s, intellectuals rolled up their sleeves, went to Detroit and Alabama, took their lumps, and helped put the movement in labor. In the fabled late '60s, the farm workers made collegiate hearts beat, and the Maoists of Progressive ... |
But for the most part, the attitude of student radicals was disdain--as in the New York teachers' strike of 1968-69, with tragic consequences that reverberate to this day. Especially because the AFL-CIO was hotter to subsidize anti-Communist unions in South America than in North Carolina, labor seemed fossilized--at be... |
Recently, things have changed a bit on campuses, with Yale's and Barnard's strikers getting sizable student support. The deeper challenge will be not just to sign up union members and bring sandwiches to picket lines but to get rusty unions to wheel around and get serious about what to propose as remedies. The days whe... |
Health insurance for all will not result from signing one company contract after another. The unions, with their immense pension funds, have to do more than look upon the economy passively while they fight rearguard battles. They have to get big and smart enough to fight for affirmative investment, child care, steady r... |
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DoraThis week I took a human head, a confused and frightened baby, some pilgrims, a Victorian lady, and... some... little magical... cloaked dude... and taped them all together! In totally unrelated news, if the police contact you, we were watching So You Think You Can Dance together last night. |
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Town of SalemMurder With Friends Facebook games tend to get a bum rap for being, well, essentially human hampster wheels by and large with little actual gameplay or originality. BlankMediaGames wants to change all that with Town of Salem, a multiplayer game of stealth, strategy and role playing where you and friends ta... |
DamnedPress X to Hide Under Bed and Cry! Playing with friends is fun. Terrorizing them is better. Available for funding on IndieGoGo, Damned is a cheery little game where four players are trapped inside a hotel... and one gets to play as the malevolent entity haunting it. While survivors are searching the building for ... |
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Uh... In the alpha test, how do people join?... I can't play against myself... |
I forgot to say which game, didn't I? :) Town of Salem I meant. :D |
I just finished the Among The Sleep alpha. Wow. very interesting game. The trailer intrigued me and that little play through has me even more curious. The atmosphere was almost stifling at times in both good and bad ways. I found the climb controls a little unresponsive at times and once or twice I had no idea what I w... |
I got annoyed that there was a lot of suspense and Hitchcockian shadows and sounds without any pay off or knowledge of what I was dealing with... so after leaving the mother's bedroom I stopped caring about what was making that noise behind me and quit creeping around nervously. |
Of course, that's when I walked into the lounge room and saw the silhouetted creature in front of the grandfather clock. I think I peed a little. |
I was surprised by the warpy mirror portal under the stairs and tunnel to weird hell cottage. I thought the game was going to be all set in the house. After watching the end game promo and seeing all the other locations, this game can't be released soon enough! |
Hi mujie, sorry for the confusion. :) It doesn't look to me like you can add players in Town of Salem just yet, so I think it's limited to whoever is playing the Alpha at that time, unfortunately. |
Anybody remember "Mafia?" It was a party game where a group of people would sit in a circle, and each person would have an assigned role: killer(s), police officer, paramedic, or civilian. The killer(s) would try to kill off all the civilians, the police officer would try to discover who the killer(s) was or were befor... |
The game was played in two phases--day & night--and consisted of a lot of throwing accusations back and forth about who the killer(s) was. |
Town of Salem sounds a lot like that, only in a Facebook game. I kinda like the idea of bringing the party game to a digital form. |
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