相关论文: Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))…

A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper-pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe behavior of individual fermions which are generated as…

We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each $R$…

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an…

We define a natural basis for the algebra of $\frak{gosp}(1|2n)$-invariant differential operators on the affine superspace $\mathbb{C}^{1|2n}$. We prove that these operators lie in the image of the centre of the enveloping algebra of…

As I briefly review, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model. I argue that the noncommutative (Moyal)…

The principle of S-duality is used to incorporate gaugino condensates into effective supergravity (superstring) Lagrangians. We discuss two implementations of S-duality which differ in the way the coupling constant is transformed. Both…

This is a review of our previous works (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power of the universal enveloping algebra of a simple Lie algebra…

We try to construct a model in which supersymmetry and grand unified gauge symmetry are dynamically broken at the same time. In this model SUSY breaking is mediated mainly by massive vector multiplet, and a new solution for the mu problem…

New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it…

The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of…

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter…

We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra $U_{q}[gl(2/2)]$ at generic deformation parameter $q$. As in the non-deformed case the finite-dimensional…

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation…

We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…

QCD justification of SU(m/n) supergroups are shown to provide a basis for the existence of an approximate hadronic supersymmetry. Effective Hamiltonian of the relativistic quark model is derived, leading to hadronic mass formulae in…

We obtain by superfield methods the exceptional representations of the OSp(2N/4,R) and SU(2,2/1) superalgebras which extend to supersingletons of SU(2,2/2N) and F(4), respectively. These representations describe superconformally coupled…

Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial…

We present various oscillator representations of the q-deformed su(1,1) algebra such as the Holstein-Primakoff, the Dyson, the Fock-Bargmann, the anyonic, and the parabose oscillator representations and discuss their coherent states with…