Quiz:Linear representation theory of symmetric group:S3

For background, see linear representation theory of symmetric group:S3.

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Basic stuff
Up to equivalence, there are three irreducible representations of symmetric group:S3 in characteristic zero: the one-dimensional trivial representation, the one-dimensional sign representation (that sends every permutation to its sign), and the standard representation of symmetric group:S3, a two-dimensional representation.

{Which of the irreducible representations is realized over the field of rational numbers? - trivial representation only - trivial representation and sign representation only + all three representations
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{Which of the irreducible representations can be realized using orthogonal matrices (i.e., matrices in the orthogonal group for the standard dot product) over the field of rational numbers? - trivial representation only + trivial representation and sign representation only - all three representations
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{The tensor product of the standard representation and the sign representation is a representation of the symmetric group of degree three. What representation is it? + the standard representation - the sum of the trivial and the sign representation - the sum of two copies of the sign representation - the sum of two copies of the trivial representation
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{The symmetric group of degree three can also be viewed as a dihedral group of degree three and order six, acting on a set of size three. The 3-cycles become rotations and the transpositions become reflections. This defines a two-dimensional representation over the real numbers. Which of these is the two-dimensional representation? + the standard representation - the sum of the trivial and the sign representation - the sum of two copies of the sign representation - the sum of two copies of the trivial representation
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