Roe Goodman

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p.17, after exercise 10. Insert the following exercises: 11. Assume that (ρ, V) is an irreducible regular representation of the linear algebraic group G. Fix v * ∈ V * with v * = 0. For v ∈ V let ϕ v ∈ Aff(G) be the representative function ϕ v (g) = v * , ρ(g)v. Let E = {ϕ v : v ∈ V } and let T : V → E be the map T v = ϕ v. Prove that T is a bijective(More)
Themes (A) Matrix factorization algorithms ↔ geometry of Lie groups and symmetric spaces: 1. Gaussian factorization with pivots ↔ cell decomposition of Flag Manifolds 2. QR factorization ↔ Horospherical coordinates on symmetric space 3. Singular value decomposition ↔ Polar coordinates on symmetric space (B) Matrix Factorizations integrate some Hamiltonian(More)
1. ALICE AND THE MIRRORS. Let us imagine that Lewis Carroll stopped condensing determinants long enough to write a third Alice book called Alice Through Looking Glass After Looking Glass. The book opens with Alice in her chamber in front of a peculiar cone-shaped arrangement of three looking glasses. She steps through one of the looking glasses and finds(More)
We study in this paper the restricted roots for a class of spherical homogeneous spaces of semisimple groups which includes simply connected symmetric spaces. For these spaces we give a detailed description (case by case) of the set of roots of the group associated with each restricted root of the space (the nest of the restricted root). As an application,(More)
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