Integral Representations of the Macdonald Symmetric Functions
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
q-alg↗
arXiv subjects
Hidetoshi Awata
Publications and source records attributed to Hidetoshi Awata.
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.
q-alg↗
Exchange Relations for the q-Vertex Operators of $U_q(\widehat{sl2})$
We consider the q-deformed Knizhnik-Zamolodchikov equation for the two point function of q-deformed vertex operators of $U_q(sl_2^)$. We give explicitly the fundamental solutions, the connection matrices and the exchange relations for the q-vertex operators of spin 1/2 and $j \in {1\over 2}{\bf Z}_{\geq 0}$. Consequently, we confirm that the connection matrices are equivalent to the elliptic Boltzman weights of IRF type obtained by the fusion procedure from ABF models.
hep-th↗
Screening Currents Ward Identity and Integral Formulas for the WZNW Correlation Functions
We derive, based on the Wakimoto realization, the integral formulas for the WZNW correlation functions. The role of the ``screening currents Ward identity'' is demonstrated with explicit examples. We also give a more simple proof of a previous result.
hep-th↗