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Quantum exceptional group G_2 and its semisimple conjugacy classes

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journal contribution
posted on 2019-07-30, 13:35 authored by Alexander Baranov, Andrey Mudrov, Vadim Ostapenko
We construct quantization of semisimple conjugacy classes of the exceptional group G = G2 along with and by means of their representations on highest weight modules over the quantum group Uq(g). With every point t of a fixed maximal torus we associate a highest weight module Mt over Uq(g) and realize the quantized polynomial algebra of the class of t by linear operators on Mt . Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.

Funding

This study is supported in part by the RFBR grant 15-01-03148.

History

Citation

Algebras and Representation Theory, 23, 1827–1848 (2020).

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Algebras and Representation Theory

Volume

23

Pagination

1827–1848

Publisher

Springer (part of Springer Nature)

issn

1386-923X

Acceptance date

2019-07-09

Copyright date

2019

Available date

2019-08-06

Language

en

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