Evaluation Modules for Quantum Toroidal (Formula Presented) Algebras

Boris Feigin; Michio Jimbo; Evgeny Mukhin

doi:10.1007/978-3-030-63849-8_12

Evaluation Modules for Quantum Toroidal (Formula Presented) Algebras

Boris Feigin
, Michio Jimbo
, Evgeny Mukhin^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

3 Scopus citations

Abstract

The affine evaluation map is a surjective homomorphism from the quantum toroidal (Formula Presented) to the quantum affine algebra (Formula Presented) at level κ completed with respect to the homogeneous grading, where q₂ = q² and q3n=κ2. We discuss En′(q1,q2,q3) evaluation modules. We give highest weights of evaluation highest weight modules. We also obtain the decomposition of the evaluation Wakimoto module with respect to a Gelfand–Zeitlin-type subalgebra of a completion of En′(q1,q2,q3), which describes a deformation of the coset theory (Formula Presented).

Original language	English
Title of host publication	Progress in Mathematics
Publisher	Birkhauser
Pages	393-425
Number of pages	33
DOIs	https://doi.org/10.1007/978-3-030-63849-8_12
State	Published - 2021
Externally published	Yes

Publication series

Name	Progress in Mathematics
Volume	337
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

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Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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10.1007/978-3-030-63849-8_12

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abstract = "The affine evaluation map is a surjective homomorphism from the quantum toroidal (Formula Presented) to the quantum affine algebra (Formula Presented) at level κ completed with respect to the homogeneous grading, where q2 = q2 and q3n=κ2. We discuss En′(q1,q2,q3) evaluation modules. We give highest weights of evaluation highest weight modules. We also obtain the decomposition of the evaluation Wakimoto module with respect to a Gelfand–Zeitlin-type subalgebra of a completion of En′(q1,q2,q3), which describes a deformation of the coset theory (Formula Presented).",

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Evaluation Modules for Quantum Toroidal (Formula Presented) Algebras

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