What Do You Know About Hecke Algebra?

10 Questions | Total Attempts: 102

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What Do You Know About Hecke Algebra?

Hecke algebra refers to several algebras such as Iwahori–Hecke algebra of a Coxeter group, Hecke algebra of a pair, Hecke algebra of a finite group, Hecke algebra acting on modular forms, Hecke algebra of a locally compact group. See if you can ace this quiz on the almighty Hecke algebra.


Questions and Answers
  • 1. 
    Which Hecke algebra can be used to prove Macdonald's term conjecture for Macdonald polynomials?
    • A. 

      Affine

    • B. 

      Weyl

    • C. 

      Parabolic

    • D. 

      Paraholic

  • 2. 
    What is an abstract group that admits a formal description in terms of reflections  or kaleidoscopic mirrors?
    • A. 

      Symmetry group

    • B. 

      Affine group

    • C. 

      Coxeter group

    • D. 

      Weyl group

  • 3. 
    A polyhedron whose symmetry group acts transitively on its flags is?
    • A. 

      Conic

    • B. 

      Concave

    • C. 

      Irregular

    • D. 

      Regular

  • 4. 
    What is a geometric setting in which two parameters are required to determine the position of a point?
    • A. 

      Plane

    • B. 

      Two-dimensional space

    • C. 

      Bi-plane

    • D. 

      Slope

  • 5. 
    What is a well-behaved function from a topological group to the complex numbers which is invariant under the action of a discrete subgroup of the topological group?
    • A. 

      Finitive group

    • B. 

      Compact group

    • C. 

      Automorphic form

    • D. 

      Cosets

  • 6. 
    A net in a ring that acts as a substitute for an identity element is?
    • A. 

      A net identity

    • B. 

      An approximate identity

    • C. 

      A limit identity

    • D. 

      An approximate limit

  • 7. 
    If a collection of elements of a star-algebra is closed under the involution operation, it is?
    • A. 

      Linear

    • B. 

      Involuted

    • C. 

      Adjoint

    • D. 

      Self-adjoint

  • 8. 
    A linear operator on a Hilbert space is called self-adjoint if it is equal to its own?
    • A. 

      Adjoint

    • B. 

      Inverse

    • C. 

      Involution

    • D. 

      Operator

  • 9. 
    What is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure?
    • A. 

      Compact group

    • B. 

      Lie group

    • C. 

      Hecke group

    • D. 

      Compact projector

  • 10. 
    An isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive is a?
    • A. 

      Synthetic field

    • B. 

      Pair group

    • C. 

      Homography

    • D. 

      Lie group

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