What Do You Know About Schur–weyl Duality?
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.
- 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
Questions: 12 | Attempts: 5566639 | Last updated: Mar 22, 2022
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