Abstract
We consider a trace of the n-point operator \(\phi _{\mu _1\cdots \mu _n}(z_1,\cdots ,z_n)\) over the level-1 highest weight representations and show that it satisfies the face type, i.e. dynamical elliptic q-KZ equation. A key to this is a cyclic property of trace and the exchange relation of the vertex operators. Evaluating the trace explicitly we also give an elliptic hypergeometric integral solution to the equation (Konno, J. Integrable Syst. 2, 1–43 (2017)).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Aganagic, A. Okounkov, Elliptic Stable Envelopes. Preprint (2016). arXiv:1604.00423
J.-S. Caux, H. Konno, M. Sorrell, R. Weston, Tracking the effects of interactions on spinons in gapless Heisenberg chains. Phys. Rev. Lett. 106, 217203 (4 p.) (2011)
J.-S. Caux, H. Konno, M. Sorrell, R. Weston, Exact form-factor results for the longitudinal structure factor of the massless XXZ model in zero field. J. Stat. Mech., P01007 (40 p.) (2012)
O. Foda, M. Jimbo, T. Miwa, K. Miki, A. Nakayashiki, Vertex operators in solvable lattice models. J. Math. Phys. 35, 13–46 (1994)
T. Kojima, H. Konno, R. Weston, The vertex-face correspondence and correlation functions of the fusion eight-vertex models I: The general formalism. Nucl. Phys. B720, 348–398 (2005)
H. Konno, Elliptic weight functions and elliptic q-KZ equation. J. Integrable Syst. 2, 1–43 (2017). https://doi.org/10.1093/integr/xyx011
H. Konno, Elliptic stable envelopes and finite-dimensional representations of elliptic quantum group. J. Integrable Syst. 3, 1–43 (2018). https://doi.org/10.1093/integr/xyy012
P. Koroteev, P. Pushkar, A. Smirnov, A. Zeitlin, Quantum K-theory of Quiver Varieties and Many-body Systems. Preprint (2017). arXiv:1705.10419
M. Lashkevich, Y. Pugai, Free field construction for correlation functions of the eight-vertex model. Nucl. Phys. B516, 623–651 (1998)
S. Lukyanov, Y. Pugai, Multi-point local height probabilities in the integrable RSOS model. Nucl. Phys. B473, 631–658 (1996)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Konno, H. (2020). Elliptic q-KZ Equation. In: Elliptic Quantum Groups. SpringerBriefs in Mathematical Physics, vol 37. Springer, Singapore. https://doi.org/10.1007/978-981-15-7387-3_8
Download citation
DOI: https://doi.org/10.1007/978-981-15-7387-3_8
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-7386-6
Online ISBN: 978-981-15-7387-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)