Jan 30, 2020 · I am trying to understand the dual representation. But I am struggling to understand even the definition. Let $\\rho: G \\to GL(V)$ be a representation of a finite group. …

The dual space is the set of linear functionals on the vector space. The only obvious way to define a representation on the dual space is by taking a given functional and precomposing it with the …

Sep 9, 2020 · The dual representation is, as its name suggests, naturally defined on the dual V ∗, not on V; that is, it's ρ: G → GL(V ∗). The fact that you mix taking the abstract dual with …

Nov 24, 2014 · Character of dual Representation? Ask Question Asked 11 years, 1 month ago Modified 6 years, 8 months ago

The natural bilinear pairing between V∗ V ∗ and V V is the pairing f, v =f(v) f, v = f (v) for each f ∈V∗ f ∈ V ∗ and each v ∈ V v ∈ V. The equality means we want the representation of V V and …

Jan 6, 2019 · For a semisimple Lie Algebra g g with Cartan Subalgebra t t, let V(λ) V (λ) be the unique irreducible highest weight module with highest weight λ λ. I am asked to show that the …

Jul 28, 2015 · Dual space isomorphism and the dual representation Ask Question Asked 10 years, 5 months ago Modified 10 years, 5 months ago

Nov 24, 2015 · The ordered bases of V and W induce ordered dual bases on the dual spaces V ∗ and W ∗, so the transformation A ∗ may also be represented by a matrix with respect to them - …

Jun 1, 2020 · Dual representation of finite groups Ask Question Asked 5 years, 6 months ago Modified 5 years, 6 months ago

Aug 19, 2019 · This is called the dual representation of V V. Very concretely, the idea is that we need to both take inverses and take duals (two operations which reverse the order of …