What Do You Know About Schur Functors?

10 Questions | Total Attempts: 103

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What Do You Know About Schur Functors?

In the science of structure, order, and relation otherwise known as mathematics, the field of representation theory encompasses Schur functors, which are particular functors from the classification of modules over a settled commutative ring to itself. They are indexed by partitions and applicable in the context of Schur-Weyl duality and Specht module amongst others.


Questions and Answers
  • 1. 
    Which power of a vector space do they generalize?
    • A. 

      Interior power

    • B. 

      Symmetric power

    • C. 

      Asymmetric power

    • D. 

      Fusion power

  • 2. 
    In which sort of space is it applied? 
    • A. 

      Vector space

    • B. 

      Scalar space

    • C. 

      Vector—Scalar space

    • D. 

      Geometric space

  • 3. 
     What are used to index the Schur functors? 
    • A. 

      Young diagrams

    • B. 

      Diagrammatic functions

    • C. 

      Brandon indexes

    • D. 

      Crystal structures

  • 4. 
     Which ring is associated with the theorem? 
    • A. 

      Associative ring

    • B. 

      Distributive ring

    • C. 

      Commutative ring

    • D. 

      Fixed ring

  • 5. 
    What does the horizontal diagram with n cells correspond to?
    • A. 

      Nth interior power functor

    • B. 

      Nth power functor

    • C. 

      Nth exterior power functor

    • D. 

      Nth symmetric power functor

  • 6. 
    What does the vertical diagram with n cells correspond to?
    • A. 

      Nth symmetric power functor

    • B. 

      Nth exterior power functor

    • C. 

      Nth power functor

    • D. 

      Nth interior power functor

  • 7. 
    What does V represent?
    • A. 

      Vector space

    • B. 

      Valency

    • C. 

      Velocity

    • D. 

      Vassicitude

  • 8. 
    What does R represent?
    • A. 

      Commutative ring

    • B. 

      Associative ring

    • C. 

      Fixed ring

    • D. 

      Distributive ring

  • 9. 
    Which condition satisfies a vector space V that is fixed over a field of characteristic zero? 
    • A. 

      ( V ) = Λ n( V )

    • B. 

      S λ ( V ) = Λ n( V )

    • C. 

      S λ ( V ) = n( V)

    • D. 

      S = Λ n( V )

  • 10. 
    What does ​​​​​​TGL(V) represent?
    • A. 

      Endomorphism group

    • B. 

      Pyromorphism group

    • C. 

      Interior group

    • D. 

      Automorphism group

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