Category and genus of infinite-dimensional representation spheres

1993 ◽  
pp. 30-52
Author(s):  
Thomas Bartsch
Keyword(s):  
Dimensional Representation ◽  
Infinite Dimensional ◽  
Infinite Dimensional Representation

QUASI-EXACTLY SOLVABLE PROBLEMS AND SU(1,1) GROUP

1994 ◽  
Vol 09 (16) ◽  
pp. 1501-1505 ◽  
Author(s):  
O.B. ZASLAVSKII
Keyword(s):  
Lie Algebra ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Infinite Dimensional Representation

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

COLORED BRAID MATRICES FROM INFINITE-DIMENSIONAL REPRESENTATIONS OF Uq(g)

1992 ◽  
Vol 07 (09) ◽  
pp. 767-779 ◽  
Author(s):  
TETSUO DEGUCHI ◽  
YASUHIRO AKUTSU
Keyword(s):  
Alexander Polynomial ◽  
Dimensional Representation ◽  
R Matrix ◽  
Infinite Dimensional ◽  
Vertex Models ◽  
Infinite Dimensional Representation

From a new infinite-dimensional representation of the universal R-matrix of [Formula: see text], we derive the colored braid matrices which gave generalizations of the multivariable Alexander polynomial. We propose color representations of Uq(g). We construct colored vertex models from the color representations of [Formula: see text].

Nonlinear Schrödinger Model with Boundary, Integrability and Scattering Matrix Based on the Degenerate Affine Hecke Algebra

1997 ◽  
Vol 12 (30) ◽  
pp. 5397-5410 ◽  
Author(s):  
Yasushi Komori ◽  
Kazuhiro Hikami
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Many Body ◽  
Dimensional Representation ◽  
Systematic Method ◽  
Infinite Dimensional ◽  
Nonlinear Schrödinger ◽  
Scattering Matrices ◽  
Many Body Systems ◽  
Infinite Dimensional Representation

The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang–Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

scholarly journals SOLVABILITY OF THE F4 INTEGRABLE SYSTEM

2001 ◽  
Vol 16 (29) ◽  
pp. 4769-4801 ◽  
Author(s):  
KONSTANTIN G. BORESKOV ◽  
JUAN CARLOS LOPEZ VIEYRA ◽  
ALEXANDER V. TURBINER
Keyword(s):  
Weyl Group ◽  
Differential Operators ◽  
Coupling Constants ◽  
Dimensional Representation ◽  
Algebraic Form ◽  
Finite Dimensional Representation ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Exactly Solvable ◽  
New Variables

It is shown that the F4 rational and trigonometric integrable systems are exactly-solvable for arbitrary values of the coupling constants. Their spectra are found explicitly while eigenfunctions are by pure algebraic means. For both systems new variables are introduced in which the Hamiltonian has an algebraic form being also (block)-triangular. These variables are invariant with respect to the Weyl group of F4 root system and can be obtained by averaging over an orbit of the Weyl group. An alternative way of finding these variables exploiting a property of duality of the F4 model is presented. It is demonstrated that in these variables the Hamiltonian of each model can be expressed as a quadratic polynomial in the generators of some infinite-dimensional Lie algebra of differential operators in a finite-dimensional representation. Both Hamiltonians preserve the same flag of spaces of polynomials and each subspace of the flag coincides with the finite-dimensional representation space of this algebra. Quasi-exactly-solvable generalization of the rational F4 model depending on two continuous and one discrete parameters is found.

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