Harunobu Kubo

A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.

Quantum

We derive a quantum deformation of theWN algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.

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Primary fields of the q-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields are represented by the shift operator Θξf(x) = f(ξx). Four point functions of the primary fields enjoy the connection formula associated with the Boltzmann weights of the fusion Andrews–Baxter–Forrester model.

algebras and Macdonald polynomials

Abstract It is shown that an extended q -deformed su (2) algebra with an extra (“Schwinger”) term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q -deformed algebra, we obtain functional Bethe ansatz equations whose solutions should be functions of finite degree. It is also shown that the zero energy solution is expressed in terms of an Askey-Wilson polynomial.

Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions

A difference operator realization of quantum deformed oscillator algebra ℋq(1) with a Casimir operator freedom is introduced. We show that this ℋq(1) has a nonlinear mapping to the deformed quantum su(2) which was introduced by Fujikawa et al. We also examine the cyclic representation obtained by this difference operator realization and the possibility to analyze a Bloch electron problem by ℋq(1).

An extended q-deformed su(2) algebra and the Bloch electron problem

An extra term generally appears in the q-deformed su(2) algebra for the deformation parameter q=exp2π iθ, if one combines the Biedenharn–Macfarlane construction of q-deformed su(2), which is a generalization of Schwingers construction of conventional su(2), with the representation of the q-deformed oscillator algebra which is manifestly free of negative norm. This extra term introduced by the requirement of positive norm is analogous to the Schwinger term in current algebra. Implications of this extra term on the Bloch electron problem analyzed by Wiegmann and Zabrodin are briefly discussed.

Oscillator Quantum Algebra and Deformed su(2) Algebra

Abstract H β was measured in the interaction of hydrogen plasma stream with various gases and it showed the highest intensity when the target gas in helium. This is attributed to the dissociative excitation transfer between excited helium atoms and hydrogen molecules.