Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type

QI Huan-ge, CHENG Yong-sheng, WANG Meng-ping, WU Lin-li

doi:10.13371/j.cnki.chin.q.j.m.2016.04.001

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 4: 331 - 339

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.04.001

Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type

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1. School of Mathematics and Statistics,Henan University2. Institute of Contemporary Mathematics,Henan University

CHENG Yong-sheng(corresponding author)(1973-), male, native of Lankao, Henan, an associate professor of Henan University, Ph.D., engages in Lie theory.

Received date: 2016-01-28

Online published: 2020-10-30

Supported by

Supported by the National Natural Science Foundation of China(11047030)； Supported by the Science and Technology Program of Henan Province(152300410061)；

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Abstract

We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.

Key words： the q-deformed Virasoro algebra of Hom-type; unitary highest weight representation; Kac determinant formula

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QI Huan-ge, CHENG Yong-sheng, WANG Meng-ping, WU Lin-li . Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(4) : 331 -339 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.001

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