Examples
All representation of the symmetric groups are real (and in fact rational), since we can build a complete set of irreducible representations using Young tableaux.
All representations of the rotation groups are real, since they all appear as subrepresentations of tensor products of copies of the fundamental representation, which is real.
Further examples of real representations are the spinor representations of the spin groups in 8k−1, 8k, and 1 + 8k dimensions for k = 1, 2, 3 ... . This periodicity modulo 8 is known in mathematics not only in the theory of Clifford algebras, but also in algebraic topology, in KO-theory; see spin representation.
Read more about this topic: Real Representation
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)