nLab induced representation > adjoint

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M x G-equivariant vector bundle F, π1: F → M Representation R(F) of H on π1–1(x) h π1 h π1 h π1 h G / H G-equivariant vector bundle L(V), π2: (G×V) / H → G / H Representation s of H on V h π2 h π2 h π2 h R Restrict to action of H on a single fiber π1–1(x) L Construct induced bundle h ⋅ (g, v) = (g h–1, s(h)v) π2: (G×V) / H → G / H π2(〚(g, v)〛) = g H g1 ⋅ 〚(g, v)〛 = 〚(g1g, v)〛 Intertwiner i* i* : π1–1(x) → V i* h = h i* Intertwiner i i : V →π1–1(x) i h = h i Vector bundle morphism (f*, m*) f* : F → L(V) m* : M → G / H m* π1 = π2 f* f* g = g f* Vector bundle morphism (f, m) f : L(V) → F m : G / H → M m π2 = π1 f f g = g f

Last revised on November 30, 2015 at 03:54:45. See the history of this page for a list of all contributions to it.

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