What Do You Know About Satake Isomorphism?

10 Questions | Total Attempts: 103

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What Do You Know About Satake Isomorphism?

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.


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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