What Do You Know About Schur–weyl Duality?

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What Do You Know About Schurweyl Duality? - Quiz

In the representation theory branch of mathematics, Schur–Weyl duality relates unchangeable limited dimensional representations of the general symmetric and linear groups and gatherings. The mathematical theorem shapes a prototype circumstance in representation hypothesis including two sorts of symmetry that decide each other. To know more about Schur–Weyl duality, take this short quiz.


Questions and Answers
  • 1. 
    Which theorem is used to prove the Schur–Weyl duality? 
    • A. 

      Double centralizer theorem

    • B. 

      Fenz theorem

    • C. 

      Optimum centralized theorem

    • D. 

      Colligated theorem

  • 2. 
    How many symmetries are involved in the puzzle? 
    • A. 

      2

    • B. 

      4

    • C. 

      6

    • D. 

      8

  • 3. 
    Which of these does S(k) represent?
    • A. 

      Symmetry group

    • B. 

      Symbol representation

    • C. 

      Synchronization group

    • D. 

      Keptic group

  • 4. 
    Which of these does GL(n) represent?
    • A. 

      Sequential number

    • B. 

      Geometrical linear number

    • C. 

      Geographical linear number

    • D. 

      General linear number

  • 5. 
    Which kind of information is the puzzle used for?
    • A. 

      Scientific information

    • B. 

      Mechanics information

    • C. 

      Quantum information

    • D. 

      Earth-related study

    • E. 

      Energetics information

  • 6. 
    What are the representations of the symmetric group?
    • A. 

      Trivial representation and geometric representation

    • B. 

      Sign representation and trivial representation

    • C. 

      Mesh representation and sign representation

    • D. 

      Fibonacci representation and sign representation

  • 7. 
    How do you represent k=2 and n>1?
    • A. 

      The space of two tensors decomposes into one part

    • B. 

      The space of two tensor decomposes into two parts

    • C. 

      The space of one tensor decomposes into halves

    • D. 

      The space of two tensor remain unchanged

  • 8. 
    What is the result of the trivial representation of S2? 
    • A. 

      Symmetric tensors

    • B. 

      Asymmetric tensors

    • C. 

      Both symmetric and asymmetric tensors

    • D. 

      Tangential tensors

  • 9. 
    Who discovered the puzzle?
    • A. 

      Hermann Schur and Issai Weyl

    • B. 

      Hermann Weyl and Issai Schur

    • C. 

      Mattias Weyl and Isaac Schur

    • D. 

      Matthew Weyl and John Schur

  • 10. 
    What are the major groups used for determining the puzzle?
    • A. 

      Linear and Symmetric

    • B. 

      Geometric and Arithmetic

    • C. 

      Finite and infinite

    • D. 

      Inequality and Assymetric

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