What Do You Know About The Hecke Algebra Of A Pair?

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What Do You Know About The Hecke Algebra Of A Pair?

Hecke algebra of a pair, or Hecke pair as it is shortly called, consists of an approximate pair of identity, whose approximate modules of unital value are the same as the K-finite representation of the pairs. The algebra usually appears with k being a compact subgroup of a Lie group that has a Lie algebra g. To properly understand Hecke algebra, there is a need for certain preliminary knowledge. This short quiz will give some idea about Hecke algebra in general.


Questions and Answers
  • 1. 
    Hecke algebra was studied by who? 
    • A. 

      Erich Hecke

    • B. 

      Hecke Iwahori

    • C. 

      Schur Hecke

    • D. 

      Erich Schur

  • 2. 
    Hecke algebra has which of the following subgroups? 
    • A. 

    • B. 

      G

    • C. 

      F

    • D. 

      X

  • 3. 
    How can the algebra also be interpreted? An algebra of...
    • A. 

      Minor cosets

    • B. 

      Major cosets

    • C. 

      Subsets

    • D. 

      Double cosets

  • 4. 
    Who studied Hecke ring? 
    • A. 

      Ian Grey

    • B. 

      Ian McDonald

    • C. 

      George Lusztig

    • D. 

      None of the above

  • 5. 
    When we start with a Gelfrand pair in Hecke algebra, what is the resulting algebra called?
    • A. 

      Additive

    • B. 

      Gelfrand equation

    • C. 

      Commutative

    • D. 

      Hecke equation

  • 6. 
    Which of the following is a finite-dimensional smooth manifold G with a group of structure on the manifold? 
    • A. 

      Lie group

    • B. 

      Morphism

    • C. 

      Invariants

    • D. 

      Convolutions

  • 7. 
    What is a convolution?
    • A. 

      A geometric analysis to produce data

    • B. 

      An equatuonal analysis to get data

    • C. 

      A mathematical operation to derive third equation from two equations

    • D. 

      A mathematic operation to get numerical solution to equations

  • 8. 
    What is the reverse of a convolution operation? 
    • A. 

      Reverse convolution

    • B. 

      Unconvolution

    • C. 

      Deconvolution

    • D. 

      Infinite convolution

  • 9. 
    Convolutions cannot be applied in which of these? 
    • A. 

      Genetics

    • B. 

      Statistics

    • C. 

      Mathematics

    • D. 

      Engineering

  • 10. 
    Under involution operations, a closed collection of elements of a star-algebra is known as what?
    • A. 

      Adjust

    • B. 

      Linear

    • C. 

      Self-adjoint

    • D. 

      Involuted

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