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- Roe Goodman, Nolan R Wallach
- 1999

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)

Dedicated to the memory of Irving E. Segal, who introduced me to the beauties and mysteries of representation theory.

- Roe Goodman, Nolan R Wallach
- 2009

- Roe Goodman
- 1999

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)

- Simon Gindikin, Roe Goodman
- 2012

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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