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.… Expand

AbstractThe Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been… Expand

For 11 examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux–Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be… Expand

We study an extension of N = 2 superconformal algebra by the addition of the spectral flow generators. We present the extended algebra corresponding to complex 3-dimensional Calabi-Yau manifold and… Expand

We obtain an explicit expression for the defining relation of the deformed WN algebra, DWA(ŝlN)q,t. Using this expression we can show that, in the q → 1 limit, DWA(ŝlN)q,t with t = e 2πi N q k+N N… Expand