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

@article{Shiraishi1996AQD, title={A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions}, author={Jun'ichi Shiraishi and Harunobu Kubo and Hidetoshi Awata and Satoru Odake}, journal={Letters in Mathematical Physics}, year={1996}, volume={38}, pages={33-51} }

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.

## 264 Citations

A Coset-Type Construction for the Deformed Virasoro Algebra

- Mathematics
- 1997

An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra Uq(sl2). A similar construction is…

Whittaker Vector of Deformed Virasoro Algebra and Macdonald Symmetric Functions

- Mathematics
- 2014

We give a proof of Awata and Yamada’s conjecture for the explicit formula of Whittaker vector of the deformed Virasoro algebra realized in the Fock space. The formula is expressed as a summation over…

Deformed Virasoro Algebras from Elliptic Quantum Algebras

- Mathematics
- 2016

We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact…

Note on the algebra of screening currents for the quantum-deformed W-algebra

- Mathematics
- 1997

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra can be put together to form a single algebra which can be…

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

- Mathematics
- 1996

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…

The Integrals of Motion for the Deformed Virasoro Algebra

- Mathematics
- 2007

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed Virasoro algebra. We call one of them local integrals and the other nonlocal one, since they can…

Norm of the Whittaker vector of the deformed Virasoro algebra

- Mathematics
- 2014

We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov.…

Quantum Deformation of the WN Algebra y

- Physics
- 1996

We review the WN algebra and its quantum deformation, based on free eld realizations. The (quantum deformed) WN algebra is dened through the (quantum deformed) Miura transformation, and its singular…

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