Twisted affine Lie superalgebras and integrability

A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types X = A ( 2 m − 1 , 2 n − 1 ) ( 2 ) ( m , n ≠ 0 , ( m , n ) ≠ ( 1 , 1 ) ), A ( 2 m , 2 n ) ( 4 ) ,   A ( 2 m , 2 n − 1 ) ( 2 ) or D ( m + 1 , n ) ( 2 ) ( m ≥ 0 , n > 0 ). It is known that irreducible int...

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Bibliographic Details
Published in:Communications in algebra 2024-08, Vol.52 (8), p.3643-3654
Main Author: Yousofzadeh, Malihe
Format: Article
Language:English
Subjects:
Finite weight modules
integrable modules
Lie groups
Modules
twisted affine Lie superalgebras
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Summary:A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types X = A ( 2 m − 1 , 2 n − 1 ) ( 2 ) ( m , n ≠ 0 , ( m , n ) ≠ ( 1 , 1 ) ), A ( 2 m , 2 n ) ( 4 ) ,   A ( 2 m , 2 n − 1 ) ( 2 ) or D ( m + 1 , n ) ( 2 ) ( m ≥ 0 , n > 0 ). It is known that irreducible integrable highest weight modules over a twisted affine Lie superalgebra of type X do not exist if m ≠ 0. In this paper, we show that nonzero level irreducible integrable finite weight modules over a twisted affine Lie superalgebra of type X do not exist if m ≠ 0.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2326070