How Much Do You Know About Alvis-curtis Duality?

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How Much Do You Know About Alvis-curtis Duality?

Most of the theories that we use today in mathematics are most of the time very old. It is as if all has already been invented or deciphered when it comes to math. Well, Alvis Curtis has proven us wrong because in the 1990s he came up with a new and bright theory. It is described as a duality operation on the characters of a reductive group over a finite field. So, how much do you know about it? Take our quiz and find out.


Questions and Answers
  • 1. 
    What's duality?
    • A. 

      It's a group of mathematical structures into other concepts.

    • B. 

      It's a group of theorems into other concepts.

    • C. 

      It's a group of operations into other concepts.

    • D. 

      It's a group of concepts, theorems/mathematical structures into other concepts.

  • 2. 
    What is a (B, N) pair?
    • A. 

      It is a structure or groups of Lie type that allows 2 to give uniform proofs of many results.

    • B. 

      It is a structure or groups of Lie type that allows 3 to give uniform proofs of many results.

    • C. 

      It is a structure or groups of Lie type that allows 4 to give uniform proofs of many results.

    • D. 

      It is a structure or groups of Lie type that allows 1 to give uniform proofs of many results.

  • 3. 
    What's a parabolic induction?
    • A. 

      It's a method of constructing representation of a reductive group from representation of its common subgroups.

    • B. 

      It's a method of constructing representation of a inclusive group from representation of its parabolic subgroups.

    • C. 

      It's a method of constructing representation of a reductive group from representation of its parabolic subgroups.

    • D. 

      It's a method of constructing representation of a reductive group from representation of its subgroups.

  • 4. 
    What's the other term for Steinberg representation?
    • A. 

      Steinberg plan

    • B. 

      Steinberg module

    • C. 

      Steinberg multiplication

    • D. 

      Steinberg addition

  • 5. 
    What's the other term for cuspidal representation?
    • A. 

      Cuspidal identity

    • B. 

      Cuspidal formula

    • C. 

      Cuspidal division

    • D. 

      Cuspidal character

  • 6. 
    What's the Gelfand-Graev representation?
    • A. 

      It's a representation of a reductive group over a infinite field.

    • B. 

      It's a representation of a inclusive group over a finite field.

    • C. 

      It's a representation of a reductive group over a finite field.

    • D. 

      It's a representation of a reductive group over a great field.

  • 7. 
    What is the Alvis Curtis Duality?
    • A. 

      It is an isometry on generalized addition

    • B. 

      It is an isometry on generalized multiplication

    • C. 

      It is an isometry on generalized functions

    • D. 

      It is an isometry on generalized characters

  • 8. 
    What's an idempotent?
    • A. 

      It denotes an element of a set that is unchanged in value when multiplied or otherwise operated on by itself.

    • B. 

      It denotes several elements of a set that is unchanged in value when multiplied or otherwise operated on by itself.

    • C. 

      It denotes 10 elements of a curve that is unchanged in value when added or otherwise operated on by itself.

    • D. 

      It denotes an element of on a curve that is unchanged in value when divided or otherwise operated on by itself.

  • 9. 
    Who invented the Alvis Curtis duality?
    • A. 

      Charles W.Curtis

    • B. 

      Dean Alvis

    • C. 

      Kawanaka

    • D. 

      Carter

  • 10. 
    In what years was this theory invented?
    • A. 

      1979

    • B. 

      1980

    • C. 

      1950

    • D. 

      1880