What Do You Know About Satake Isomorphism?

10 Questions | By AdeKoju | Updated: Mar 18, 2022 | Attempts: 117

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What Do You Know About Satake Isomorphism? - Quiz

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.

Questions and Answers

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