ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 58, 35 Goloubeva, Valentina, VINITI, Moscow, Russian Federation On algebraic similarity of Calogero and Sutherland models For a given root system R on Bethe–Dunkl subvarieties of ℂ^{N}, N = #R, the spin operators of Calogero and Sutherland type H_{C,S} = −Δ + V are considered where Δ are the corresponding Laplace operators and V are the potentials. The Fock algebras A_{S,C} and corresponding Weyl–Heisenberg spaces F_{S,C} as 1-dimensional modules over these algebras are constructed and the homomorphisms ρ_{A} : A_{S} → A_{C} and ρ_{C} : F_{S} → F_{C} are defined such that H_{S} is transformed into Ĥ_{C} = H_{C} + Q, Q = ∑_{α,β} F (α, β)u_{α}u_{β}. F (α, β) is a bilinear form associated to a given root system, u_{α} ∈ ℂ^{N}. The eigenfunctions of conjugate to H_{S} (so called Jack polynomials) under homomorphism ρ correspond to the eigenfunctions of Ĥ_{C} (so called Hidden Jack polynomials).