Quiz About Affine Hecke Algebra

10 Questions | By Ruso | Last updated: Mar 22, 2022 | Total Attempts: 109

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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