Representations of the q-Klein-bottle Lie algebra

Autor:	Jingjing Jiang
Rok vydání:	2022
Předmět:	Pure mathematics Algebra and Number Theory Verma module Lie algebra Weight space Mathematics::Representation Theory Central charge Klein bottle Mathematics
Zdroj:	Journal of Algebra. 591:36-58
ISSN:	0021-8693
DOI:	10.1016/j.jalgebra.2021.10.028
Popis:	We give the necessary and sufficient conditions for all weight spaces of the highest weight irreducible module V ( ϕ ) of the q-Klein-bottle Lie algebra B to be finite dimensional. We prove that the irreducible highest weight module V ( ϕ ) equals to the Verma B -module V ¯ ( ϕ ) if and only if V ( ϕ ) has at least one infinite-dimensional weight space. We also give the maximal proper submodule of the Verma module V ¯ ( ϕ ) and the e-character of the irreducible highest weight B -module V ( ϕ ) when the highest weight ϕ satisfies some natural conditions. Furthermore, we give the classification of the Harish-Chandra B -modules with nontrivial central charge.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d79d277bbef1d5d791bf8719e79971cc https://doi.org/10.1016/j.jalgebra.2021.10.028 Zobrazit plný text záznamu Full Text from ScienceDirect