Quiz About Affine Hecke Algebra

10 Questions | Total Attempts: 109

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Quiz About Affine Hecke Algebra - Quiz

The name might sound a bit strange but the Hecke Algebra is a type of affine Weyle group. And as strange as it may also sound, people actually use it everyday. So, are you a math genius? What do you know about this theory? Take our quiz and find out.


Questions and Answers
  • 1. 
    What's an affine root system?
    • A. 

      It's a system of affine-linear function on a Euclidean space.

    • B. 

      It's a root system of affine-linear function on a space.

    • C. 

      It's a root system of affine-linear function on a Euclidean space.

    • D. 

      It's a root system of a linear function on a Euclidean space.

  • 2. 
    What's an associative algebra?
    • A. 

      It's an algebraic structure with compatible operation of addition by elements in some field.

    • B. 

      It's an algebraic structure with compatible operation of multiplication by elements in some field.

    • C. 

      It's an algebraic structure with compatible operation of addition, multiplication, and a scalar multiplication by elements in some field.

    • D. 

      It's an algebraic structure with compatible operation of addition, and a scalar multiplication by elements in some field.

  • 3. 
    What's Weyl group?
    • A. 

      It's a subgroup of isometry group of the system.

    • B. 

      It's a subgroup of metric group of the root system.

    • C. 

      It's a subgroup of isometry group of the root system.

    • D. 

      It's a subgroup of geometry group of the root system.

  • 4. 
    How is an affine Hecke algebra depicted?
    • A. 

      L (Σ, Q)

    • B. 

      H (Σ, q)

    • C. 

      Q(Σ, h)

    • D. 

      H (L,H)

  • 5. 
    Who is Ivan Cherednik?
    • A. 

      He is a French mathematician who introduced the double affine Hecke algebras

    • B. 

      He is a Russian mathematician who introduced the triple affine Hecke algebras

    • C. 

      He is a Russian technician who introduced the double affine Hecke algebras

    • D. 

      He is a Russian mathematician who introduced the double affine Hecke algebras

  • 6. 
    What's a quantum KZ equation?
    • A. 

      It's an analogue for quantum affine algebras of Knizhnik

    • B. 

      It's an analogue for affine algebras of Knizhnik

    • C. 

      It's an analogue for quantity affine algebras of Knizhnik

    • D. 

      It's an analogue for quality affine algebras of Knizhnik

  • 7. 
    What's the other term for Quantum KZ equation?
    • A. 

      Ppq

    • B. 

      Kzq

    • C. 

      Lkz

    • D. 

      Qkz

  • 8. 
    When were Macdonald polynomials introduced?
    • A. 

      In 1986

    • B. 

      In 1987

    • C. 

      In 1988

    • D. 

      In 1990

  • 9. 
    When does the affine Hecke reduce to C [W]?
    • A. 

      Q-1

    • B. 

      Q=0

    • C. 

      Q=1

    • D. 

      Q=-3

  • 10. 
    What's a multiplicity function?
    • A. 

      It's a number of spin states such as n of the N spins point in the Z direction

    • B. 

      It's a number of states such as n of the A spins point in the Z direction

    • C. 

      It's a number of spin states such as n of the N spins point in the M direction

    • D. 

      It's a number of spin states such as n of the Z spins point in the N direction

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