What Do You Know About Symplectic Representations?

10 Questions | By AdeKoju | Last updated: Mar 19, 2022 | Total Attempts: 105

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What Do You Know About Symplectic Representations? - Quiz

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)