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Results tagged with symmetric-functions
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user 10627
Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.
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Sym(V ⊕ ∧² V) isomorphic to direct sum of all Schur functors of V
Another way to think about it. It's equivalent to show that each dominant character of the Borel
occurs with multiplicity one in the polynomial algebra on wedge-2(V) + V.
Now multiplicity <= 1 becau …
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