What Do You Know About Symplectic Representations?

10 Questions | Total Attempts: 103

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What Do You Know About Symplectic Representations?

In the representation theory branch of mathematics, Symplectic representations are a Lie variable-based math on a symplectic vector space or a representation of a gathering which portrays a form or frame that is symplectic. If you would like to know more about this widespread type of representations, let's asses your knowledge of Symplectic representations.


Questions and Answers
  • 1. 
    What condition will a representation of a group G preserve ω?
    • A. 

      W(w.v,gw)=w(v,w)

    • B. 

      W(g.v,gw)=w(v,w)

    • C. 

      W(g.v,vw)=w(v,w)

    • D. 

      W(g.v,gw)=w(v,g)

  • 2. 
    Which indicator is used to identify Symplectic representations?
    • A. 

      Frobenius-schur indicator

    • B. 

      Thomas indicator

    • C. 

      Abel–Jacobi theorem

    • D. 

      Ado's theorem

  • 3. 
    Which other representations indicate Symplectic representations?
    • A. 

      Quaternionic representations of indefinite groups

    • B. 

      Thomas representations

    • C. 

      Quaternionic representations of finite groups

    • D. 

      Mathematical folding theorem

  • 4. 
    When effective or faithful representation is a representation (V , φ), what is the homomorphism φ?
    • A. 

      Injective

    • B. 

      Objective

    • C. 

      Functional

    • D. 

      Perpendicular

  • 5. 
    When V and W are vector spaces over F, equipped with representations φ and ψ of a group G, then what is an equivariant map from V to W?
    • A. 

      Vertical map

    • B. 

      Linear map

    • C. 

      Functional map

    • D. 

      Horizontal map

  • 6. 
    When α is said to be invertible, what is this called?
    • A. 

      Functional point

    • B. 

      Repression

    • C. 

      Isomorphism

    • D. 

      Dual movement

  • 7. 
    What does the definition of an irreducible representation simple imply?
    • A. 

      Dual movement

    • B. 

      Schur's lemma

    • C. 

      Division algebra

    • D. 

      Endomorphisms

  • 8. 
    When a representation is the direct sum of two proper nontrivial subrepresentations, what is it said to be?
    • A. 

      Repressed

    • B. 

      Dimensional

    • C. 

      Decomposable

    • D. 

      Rational

  • 9. 
    What do we call the situation when the duality between the circle group S 1 and the integer Z? The analysis of the...
    • A. 

      Theory of Fourier series

    • B. 

      Carter theory

    • C. 

      Birkhoff's theorem

    • D. 

      Cartan–Dieudonné theorem

  • 10. 
    Which symbol represents Symplectic vector space?
    • A. 

      (V,W)

    • B. 

      (V,U)

    • C. 

      (W, V)

    • D. 

      (S, U)

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