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doi:10.1007/s11464-021-0932-7

Front. Math. China

2021, Vol. 16

Issue (4) : 1089-1097 https://doi.org/10.1007/s11464-021-0932-7

RESEARCH ARTICLE

Classification on irreducible Whittaker modules over quantum group

U q （ s l 3, ∧ ）

Limeng XIA¹, Xiangqian GUO², Jiao ZHANG³(

)

¹. Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, China
². School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
³. Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

We define the Whittaker modules over the simply-connected quantum group $U q （ s l 3, ∧ ）$ ; where $∧$ is the weight lattice of Lie algebra $s l 3$ : Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over $U q （ s l 3, ∧ ）$ is either a highest weight module, or determined by two parameters $z ∈ ℂ $ and $γ ∈ ℂ * $ (up to a Hopf automorphism).

Keywords Quantum group simple Whittaker module Whittaker vector

Corresponding Author(s): Jiao ZHANG

Issue Date: 11 October 2021

Cite this article:

Limeng XIA,Xiangqian GUO,Jiao ZHANG. Classification on irreducible Whittaker modules over quantum group

U q （ s l 3, ∧ ）

[J]. Front. Math. China, 2021, 16(4): 1089-1097.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0932-7
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I4/1089

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