# What Do You Know About Symplectic Representations?

10 Questions | Total Attempts: 103  Settings  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.

• 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.

• 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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