# q-Virasoro/W algebra at root of unity and parafermions

@article{Itoyama2014qVirasoroWAA,
title={q-Virasoro/W algebra at root of unity and parafermions},
author={Hiroshi Itoyama and T Oota and R. Yoshioka},
journal={Nuclear Physics},
year={2014},
volume={889},
pages={25-35}
}
• Published 19 August 2014
• Physics
• Nuclear Physics
27 Citations

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## References

SHOWING 1-10 OF 53 REFERENCES
q-Virasoro algebra at root of unity limit and 2d-4d connection
• Mathematics
• 2013
We propose a limiting procedure in which, starting from the q-lifted version (or K-theoretic five dimensional version) of the (W)AGT conjecture to be assumed, the Virasoro/W block is generated in the
The Deformed Virasoro Algebra at Roots of Unity
• Mathematics
• 1998
Abstract:We discuss some aspects of the representation theory of the deformed Virasoro algebra $\virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the
STRESS–TENSOR FOR PARAFERMIONS FROM WINDING SUBALGEBRAS OF AFFINE ALGEBRAS
We discuss a realization of stress–tensor for parafermion theories following a construction for higher level affine algebras, based on the projection of the standard level-one bosonic realization on
Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Mathematics, Physics
• 2011
The conjecture about the correspondence between instanton partition functions in theN = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensi onal conformal field theories is extended to the
Construction of Gaiotto states with fundamental multiplets through degenerate DAHA
• Mathematics
• 2014
A bstractWe construct Gaiotto states with fundamental multiplets in SU(N ) gauge theories, in terms of the orthonormal basis of spherical degenerate double affine Hecke algebra (SH in short), the