What Do You Know About Satake Isomorphism?
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Algebraic braic groups mathematician Ichirō Satake introduced Satake isomorphism (along with Satake diagrams) in the early 1960s. It recognizes the Hecke algebra or polynomial math of a reductive group over a local field with a ring of constants of the Weyl group. To find out more, take this short, intelligent quiz.
- 1.When was Satake isomorphism introduced?
- A.
1963
- B.
1964
- C.
1965
- D.
1966
- 2.What does G represent?
- A.
Trojan group
- B.
Chevalley group
- C.
Chivallas group
- D.
Martins theorem
- 3.What does K represent?
- A.
Non-archimedean local field
- B.
Archimedean local field
- C.
Local field
- D.
Global field
- 4.What does O denote?
- A.
Group of integers
- B.
Ordinate value
- C.
Orifices
- D.
Ring of integers
- 5.Over a local field, which group does it identifies?
- A.
Reductive group
- B.
Recursive group
- C.
Finite group
- D.
Infinite group
- 6.When was the geometric version of the Satake isomorphism introduced?
- A.
2006
- B.
2007
- C.
2008
- D.
2009
- 7.The Satake isomorphism identifies the Grothendieck group of complex representations of which of these?
- A.
Langlands single
- B.
Langlands dual
- C.
Langlands triple
- D.
Free space
- 8.For a Satake isomorphism in characteristic p, what is K?
- A.
Special maximal compact subgroup of G (F)
- B.
Hyperspecial maximal compact subgroup of G (F)
- C.
Krystal group
- D.
Subgroup of G (F)
- 9.For a Satake isomorphism in characteristic p, what is V?
- A.
Irreducible representation of K
- B.
Reducible representation of K
- C.
Reductive representation of K
- D.
Isomorphic representation of K
- 10.Who introduced the geometric version of the Satake isomorphism?
- A.
Mirković and Vilonen
- B.
Mirković and Markus
- C.
Vivian and Vilonen
- D.
Charles and Armstrong
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