Samantha912/NLP_A2_WTH huggingface dataset:
In mathematics, the Steinberg representation, or Steinberg module or Steinberg character,  denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the 1-dimensional sign representation ε of a Coxeter or Weyl group that takes all reflections to –1.

For groups over finite fields, these representations were introduced by , first for the general linear groups, then for classical groups, and then for all Chevalley groups, with a construction that immediately generalized to the other groups of Lie type that were discovered soon after by Steinberg, Suzuki and Ree.
Over a finite field of characteristic p, the Steinberg representation has degree equal to the largest power of p dividing the order of the group.

The Steinberg representation is the Alvis–Curtis dual of the trivial 1-dimensional representation.

, , and  defined analogous Steinberg representations (sometimes called special representations) for algebraic groups over local fields. For the general linear group GL(2), the dimension of the Jacquet module of a special representation is always one.

The Steinberg representation of a finite group
The character value of St on an element g equals, up to sign, the order of a Sylow subgroup of the centralizer of g if g has order prime to p, and is zero if the order of g is divisible by p.
The Steinberg representation is equal to an alternating sum over all parabolic subgroups containing a Borel subgroup, of the representation induced from the identity representation of the parabolic subgroup.
The Steinberg representation is both regular and unipotent, and is the only irreducible regular unipotent representation (for the given prime p).
The Steinberg representation is used in the proof of Haboush's theorem (the Mumford conjecture).

Most finite simple groups have exactly one Steinberg representation. A few have more than one because they are 
groups of Lie type in more than one way.  For symmetric groups (and other Coxeter groups) the sign representation is analogous to the Steinberg representation. Some of the sporadic simple groups act as doubly transitive permutation groups so have a BN-pair for which one can define a Steinberg representation, but for most of the sporadic groups there is no known analogue of it.

The Steinberg representation of a p-adic group

, , and  introduced Steinberg representations  for algebraic groups over local fields.  showed that the different ways of defining Steinberg representations are equivalent.
 and  showed how to realize the Steinberg representation in the cohomology group H(X) of the Bruhat–Tits building of the group.

References

 Finite Groups of Lie Type: Conjugacy Classes and Complex Characters (Wiley Classics Library) by Roger W. Carter, John Wiley & Sons Inc; New Ed edition (August 1993) 

R. Steinberg,   Collected Papers, Amer. Math. Soc.  (1997)   pp. 580–586

Representation theory of algebraic groups
Finite fields
Places We Don't Know is the debut studio album by the Swedish electronic music producer Kasbo, released on 23 March 2018 through Counter Records and Family Foreign Collective.

Singles 
The album's first single, "Lay It on Me" featuring Keiynan Lonsdale, was released on 28 June 2017. The second and third singles, "Bleed It Out" featuring Nea and "Snow In Gothenburg", were released 24 October and 12 December respectively. Both songs received music videos.

The fourth single, "Aldrig Mer" featuring TENDER, was released 18 January 2018 alongside the announcement of Places We Don't Know. The fifth and sixth singles, "Your Tempo" and "Over You" featuring Frida Sundemo were released 13 February and 13 March respectively.

Tour 
On 19 January 2018, Kasbo announced several headlining shows for the Places We Don't Know Tour. On February 12, BAYNK was revealed as an opening act for several of the shows.

Track listing

References 

2018 debut albums
Kasbo albums
Mala Polana (; ) is a village northeast of Velika Polana in the Prekmurje region of Slovenia. Črnec Creek, a tributary of the Ledava, flows past the settlement.

References

External links

Mala Polana on Geopedia

Populated places in the Municipality of Velika Polana
The following lists events that happened during 1815 in Chile.

Incumbents
Royal Governor of Chile: Mariano Osorio (-26 December), Francisco Marcó del Pont (26 December)

Events

Births
20 May - Agustín Edwards Ossandón (d. 1878)

Deaths

References 

 
Chile
Chile
A Pattern of Roses is a 1972 children's novel by British author K. M. Peyton, about a mystery and a ghost. It was issued in the US under the title So Once Was I in 1975, but subsequent editions have used the original title.

The novel was made into a television film in 1983. The film was the first significant on screen role for Helena Bonham Carter; the cast also included Philip Jackson and Suzanna Hamilton.

Plot summary
While his parents are renovating a cottage in an English village, Tim Ingram uncovers a mystery about the 15-year-old boy who once lived in the house and died in 1910 (1914 in the movie). With the help of his friend Rebecca, Tim investigates, but finds events from the past being mirrored in his own life.

References

1972 British novels
British children's novels
Novels by K. M. Peyton
British novels adapted into films
1972 children's books
Oxford University Press books
Daniele Buetti (born 1955) is a Swiss visual artist who works in several modes including installation and intervention. The media he works with includes photography, sculpture, drawing, sound, video and digital forms. He is professor at University of Fine Arts Munster where he has taught since 2004. He lives and works in Zurich, Switzerland and Münster, Germany.

His work has been described as "an expression of world-weariness and the individual’s precarious existential orientation." In the 1990s Buetti's work served as a visual critiques of the consumption of beauty. This work often appropriated images of models and high-fashion consumer products from  magazines that were pierced with a ballpoint pen.

A monograph on his work, Daniele Buetti: it's all in the mind was published in 2014 by Hirmer Publishers. The volume includes essays by Buetti, Matthias Ulrich, Max Hollein, and Jane Michael.

Buetti was born in Fribourg.

Buetti's work has been widely exhibited nationally and internationally in museums and galleries including the Schirn Kunsthalle, Frankfurt and the Kunsthaus Wien. His work was the subject of a one-person show, Could a dream be enough, at the Museo Nacional Centro de Arte Reina Sophia. His work was presented in a solo exhibition at the Swiss Institute for Contemporary Art in New York City. Buetti has also exhibited his work at Helmhaus Zurich where his installation, Auf allen Knien (On All Knees) was presented.

Public collections
Collection du F.R.A.C  (Fond régional d’Art Contemporain, Provence-Alpes-côte d’Azur)
DaimlerChrysler Collection, Berlin
Elgiz Museum, Istanbul, Turkey
Fotomuseum Winterthur
Kunsthaus, Bregenz
Johnson Museum of Art, Cornell University
Migros Museum für Gegenwartskunst, Zurich
Musée de l'Elysée, Lausanne
Museum HausKonstruktiv, Zurich
ZKM, Zentrum für Kunst undMedientechnologie, Karlsruhe

References

Swiss contemporary artists
Living people
20th-century Swiss people
1955 births
Gracia–Orlová is a women's staged cycle race which takes place in the Moravian-Silesian Region of the Czech Republic and in the Silesian Voivodeship of Poland. It was created in 1987.

Since 2004, it starts in Dětmarovice. A mountain stage is competed in Kuźnia Raciborska. The finish to the final stage is located in Orlová.

Honours

Jerseys 
As of the 2013 edition:
 denotes the rider leading the race overall
 denotes the rider leading the Points classification
 denotes the rider leading the Mountains classification
 denotes the rider leading the Sprints classification

External links 
 
 Honours of Gracia-Orlová at cyclingarchives.com

Cycle races in the Czech Republic
Cycle races in Poland
Recurring sporting events established in 1987
Sport in Silesian Voivodeship
1987 establishments in Czechoslovakia
1987 establishments in Poland
Gracia-Orlová
Women's road bicycle races
Spring (season) events in the Czech Republic
Spring (season) events in Poland
Ronald Charles Mason (1912 – 5 August 2001) was an English writer of novels, biographies, literary criticism and cricket books.

Life and career
After attending King's College School, Wimbledon, Mason entered the civil service, working most of his life in the estate duty office, employed in the collection of death duties. He also had a career as a writer, beginning as a novelist of modest success before devoting his energies to cricket books. After the Second World War he completed a first-class honours degree in English from the University of London, studying externally.
 
He had trouble getting his first cricket book, Batsman's Paradise: An Anatomy of Cricketomania, published, until he sent it to Errol Holmes, the former Surrey captain, who recommended it to a publisher. His cricket books were "marked by a genuine affection for the subject as well as a flowing style".

Mason and his wife Peggie had two sons (one of whom, Nick, was a journalist for The Guardian) and a daughter.

Prose style
Mason was a master of the long sentence. Here, in Batsman's Paradise, he describes in two sentences a rare appearance in higher company for the Surrey stalwart Tom Shepherd, in a Test trial at Lord's in 1927:

That he proceeded to engage with Leyland in a stand of over 200, driving beautifully and seeming never for a moment at a loss with the wiliest bowlers in the kingdom, never surprised me for a moment; that his innings of 90 or so was very correctly singled out as one of the gems of the match was entirely right and proper and to be expected. That the selectors would never do anything about it, or that he would never get his chance to appear in any other representative matches of any kind, was almost as inevitable a corollary; and Tom Shepherd from that time forth obediently and I do not doubt quite contentedly continued to bat and bowl at the Oval, where he was known and honoured and knew his way about.

Books

Novels
 Timbermills (1939)
 The Gold Garland (1939)
 The House of the Living (1946)
 Cold Pastoral (1946)

Non-fiction
 The Spirit above the Dust: A Study of Herman Melville (1951)
 Batsman's Paradise: An Anatomy of Cricketomania (1955)
 Jack Hobbs: A Portrait of an Artist as a Great Batsman (1960)
 Walter Hammond: A Biography (1962)
 Sing All a Green Willow (1967)
 "Plum" Warner's Last Season (1970)
 Warwick Armstrong's Australians (1971)
 Ashes in the Mouth: The Story of the Bodyline Tour of 1932-33 (1982)

References

1912 births
2001 deaths
People from Thames Ditton
People educated at King's College School, London
Alumni of the University of London
English biographers
Cricket historians and writers
English male novelists
20th-century English novelists
20th-century British biographers
20th-century English male writers
English male non-fiction writers
Male biographers
The 49th Walker Cup Match will be played 2 and 3 September 2023 at Old Course at St Andrews in Scotland. It will be the 9th Walker Cup Match to be played at St Andrews and the first since 1975.

Format
On Saturday, there will be four matches of foursomes in the morning and eight singles matches in the afternoon. On Sunday, there will again four matches of foursomes in the morning, followed by ten singles matches (involving every player) in the afternoon. In all, 26 matches will be played.

Each of the 26 matches is worth one point in the larger team competition. If a match is all square after the 18th hole extra holes are not played. Rather, each side earns  a point toward their team total. The team that accumulates at least 13 points wins the competition. In the event of a tie, the previous winner retains the Cup.

Teams

Great Britain and Ireland Team
The Great Britain and Ireland team was announced on 21 August 2023. John Gough and Barclay Brown were automatically selected to the team based on their World Amateur Golf Ranking on 16 August 2023. Gough was ranked 11th and Barclay Brown 25th in this critical release. The reserves were Tyler Weaver and Caolan Rafferty.

U.S. Team
Gordon Sargent, Michael Thorbjornsen and David Ford were the first players to make the team, as the top three Americans in the World Amateur Golf Ranking as on 21 June 2023. Nick Dunlap and Caleb Surratt were added to the USA line-up on 31 July 2023. On 9 August 2023, Thorbjornsen announced that he would be withdrawing from the USA team due to a stress fracture in his back. The remaining members of the team were announced on 20 August 2023. Two alternates for the team were also announced: Maxwell Moldovan and Neal Shipley.

Note: "Rank" is the World Amateur Golf Ranking as of the start of the Cup.

References

External links
USGA site
R&A site
Golf Bible Walker Cup coverage

Walker Cup
Golf tournaments in Scotland
Walker Cup
Walker Cup
Walker Cup
Jagati railway station () is a railway station in Kushtia, Bangladesh. It was the first railway station in present-day Bangladesh.

History
Kushtia's Jagati Railway Station has been a witness to the history of the railways in Bangladesh. This is the country's first railway station. During the British period, this station was opened in 1862 to travel from Sealdah to Kushtia. In 1844, R. M Stephenson formed the East India Railway Company to build a railway line from Howrah near Kolkata to the coal-mining-rich Raniganj town of West Bengal. In 1854, the company opened a 38-km long rail line from Howrah to Hooghly. Then on September 29, 1862, the Eastern Bengal Railway opened the rail line from Kolkata to Ranaghat. Extending this line, a 53.11-km Broad gauge railway line section was unveiled on November 15 that year until Jagati in Kushtia. At that time, the first railway station of East Bengal, Jagati, was established. Later, in order to facilitate the communication between Dhaka and Kolkata, on January 1, 1871, a railway line was started from Jagati to Goalundo ghat on the banks of the Padma river in the present Rajbari District. At that time, people used to take a train from Kolkata and go to Goalundo ghat via Jagati station.

Service
Trains that run through Jagati Railway Station are mentioned below:
Modhumoti express
Tungipara express
Nakshikantha express
Local trains

References

Railway stations in Kushtia District
Railway stations in Bangladesh opened in 1862
1862 establishments in British India
The East Region was a region that competed in the Little League World Series between 1957 and 2000, until it was split into the Mid-Atlantic and New England regions in 2001.  

The East Region was inaugurated in 1957 when the LLWS first gave out Series berths to Regional winners.  The Region initially consisted of teams from Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, Vermont, and two Canadian provinces (Ontario and Quebec). A year later, in 1958, the Canada Region was created and given its own automatic berth In the LLWS. Puerto Rico briefly competed in the East Region, from 1963 through 1967, before moving to the Latin American region.  Delaware and Maryland moved to the East Region in 1968; Washington D.C., was given its own spot in the region in 1998.

Little League Baseball expanded the LLWS to sixteen teams for the 2001 Little League World Series.  The East Region was split into the Mid-Atlantic Region (Delaware, Maryland, New Jersey, New York, Pennsylvania, and Washington D.C.) and the New England Region (Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont).

Champions 1957-2000 in the East Region

The following table indicates the East Region champion and its LLWS performance in each year between 1957 and 2000.

Results by State

See also
Mid-Atlantic Region (Little League World Series)
New England Region (Little League World Series)

References

External links
 Little League Online
 East Region Historical Results

East
Defunct baseball competitions in the United States
Sports in the Eastern United States
So Early in the Spring... The First 15 Years, (or simply So Early in the Spring) is a compilation album by American singer and songwriter Judy Collins, first released as a double LP  in 1977. It peaked at No. 42 on the Billboard Pop Albums charts. The LP featured album portraits by renowned photographer Richard Avedon.

Although it is out-of-print, all the songs are available on other releases or compilations.

Track listing 
(LP Side One; Cassette Side One)
 "Pretty Polly" (on LP, not on Cassette release) (Traditional) 5:49
 "So Early, Early in the Spring" (Traditional) 3:10
 "Pretty Saro" (Traditional) 3:05
 "Golden Apples of the Sun" (William Butler Yeats, "Song of the Wandering Oengus") 3:55
 "Bonnie Ship the Diamond" (Traditional, arranged by Judy Collins) 2:17
 "Farewell to Tarwathie" (Traditional) 5:08
(LP Side Two; Cassette Side One, continued)
 "The Hostage" (Tom Paxton) 2:49
 "La Colombe" (Jacques Brel) 5:05
 "Coal Tattoo" (Billy Edd Wheeler) 3:04
 "Carry It On" (Gil Turner) 2:49
 "Bread and Roses" (Music, 1976, by Mimi Fariña; Poem, 1912, by James Oppenheim) 3:06
 "Marat/Sade" (Musical setting by Richard Peaslee, Peter Weiss, Geoffrey Skelton and Adrian Mitchell; Play by Peter Shaffer) 5:38
(LP Side Three; Cassette Side Two)
 "Special Delivery"  (Billy Mernit) 3:50
 "The Lovin' of the Game" (Pat Garvey and Victoria Garvey Armstrong) 3:05	
 "Both Sides Now" (Joni Mitchell) 3:14
 "Marieke" (Jacques Brel, Gerard Jouannest) 3:14
 "Send In The Clowns" (Stephen Sondheim) 4:01
"Bird on the Wire" (Leonard Cohen) 4:39
(LP Side Four; Cassette Side Two, continued)
 "Since You Asked" (Judy Collins) 2:34
 "Born To The Breed" (Judy Collins) 4:50
 "My Father" (Judy Collins) 5:02
 "Holly Ann" (Judy Collins)  4:47
 "Houses" (Judy Collins) 4:37
 "Secret Gardens" (Judy Collins) 5:35

Personnel
Judy Collins – vocals, guitar, piano, keyboards

Production notes
Produced by Mark Abramson, David Anderle, Jac Holzman, Ann Purtill, Arif Mardin
Engineered by Glenn Berger, John Haeny, David Jones, Jay Messina, Phil Ramone, John Wood, Shelly Yakus

References 

1977 compilation albums
Judy Collins compilation albums
Albums produced by Mark Abramson
Albums produced by Jac Holzman
Albums produced by Arif Mardin
Albums produced by David Anderle
Elektra Records compilation albums
The Tree of Seasons is a children's book written by Boyzone member Stephen Gately and published posthumously by Hodder & Stoughton in 2010. It follows the adventures of three siblings - Josh, Michael and Beth Lotts - who are on their summer holidays, and is said to be similar in style to the works of Enid Blyton, C. S. Lewis and Walt Disney.

Foreword
The foreword was written by Elton John and David Furnish.

Introduction
The book's introduction was controversial. Written by Gately's partner Andrew Cowles, Gately's family were upset at references to Sheriff Street as one of "the poorest parts of Dublin City" and "a place of civil unrest and terrorist activity". The content of the introduction prompted the Gately family to release a statement to the Sunday Independent, published on 16 May 2010, saying they "wish to make it clear that these statements are not correct and do not reflect the views of the family" and that Gately completed his secondary education and even attended college. However, in several early interviews Stephen himself confessed to leaving education to join Boyzone, and never completing his finishing exams.

Illustrations
Gately's friend, Keith Wilson, contributed black-and-white line drawings to the book.

Completion
Following Gately's death in Spain in October 2009, the final drafts of The Tree of Seasons were completed in collaboration with June Considine and Jules Williams, with Andrew Cowles writing the acknowledgements.

Promotion
Andrew Cowles embarked on an "extensive publicity campaign" following the book's publication. He appeared on The Late Late Show to discuss the book on 14 May 2010 and was nearly reduced to tears by the questions asked by presenter Ryan Tubridy. Tubridy responded to criticism by later remarking that Cowles had given "a very solid, brave interview and I know for a fact that he's happy with the way it went".

Reception
Irish Independent reviewer Sarah Webb remarked: "For a young man with no previous writing experience, the Tree of Seasons is quite an achievement" and "would make, with the addition of some powerful songs, an excellent musical".

Sunday Tribune reviewer Pat Nugent compared it to Enid Blyton's The Faraway Tree series, remarked on "a host of kinks and clumsy moments that could have been fixed with relative ease", but said there was "a distinct possibility [Gately's] career as a children's author would have outpaced his status as a popstar".

At least 10,000 copies of The Tree of Seasons were pre-ordered in Ireland and at least 5,000 copies were pre-ordered in Britain.
 
At least 3,600 people called themselves fans on Facebook on the week of its release.

The book spent 3 weeks on the UK Best Sellers list.

References

2010 Irish novels
2010 children's books
Irish children's novels
Irish fantasy novels
Children's fantasy novels
Hodder & Stoughton books
Laleli may refer to:

 Laleli, Fatih
 Laleli, Pazaryolu
 Laleli, Refahiye
 Laleli, Pazaryolu, a village in the Pazaryolu district in Eastern Turkey
Grammoxyla hieroglyphica is a species of beetle in the family Cerambycidae, and the only species in the genus Grammoxyla. It was described by Redtenbacher in 1868.

References

Xylorhizini
Beetles described in 1868
The Burgstein is a rock formation, about  high, in the valley of the Ilm in Langewiesen in the central German state of Thuringia. It is made from quartz porphyry and has been a geological natural monument since 1939.

It was formed when the Ilm carved out its valley and washed away the surrounding rock. When the Ilmenau–Großbreitenbach railway was built in 1881 it was exposed again because rock at its foot was removed in order to lay the railway track. The rock dates to the Pennsylvanian sub-period and belongs to the Möhrenbach Formation.

The origin of its name is not clear (Burgstein literally means "castle rock"). In Langewiesen, the road of Burgstein is named after the rock.

References

Rock formations of Thuringia
Natural monuments in Thuringia