What Do You Know About Satake Isomorphism?

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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

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