Kac modules of sl (2/2) and the extended Kac‐Weyl formulas | Zendy

Shakibi H. | Zendy

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Kac modules of sl (2/2) and the extended Kac‐Weyl formulas

Author(s) -

Shakibi H.

Publication year - 1992

Publication title -

mathematika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.955

H-Index - 29

eISSN - 2041-7942

pISSN - 0025-5793

DOI - 10.1112/s0025579300006823

Subject(s) - mathematics , lie superalgebra , simple (philosophy) , simple module , verma module , pure mathematics , character (mathematics) , superalgebra , weyl group , algebra over a field , combinatorics , lie algebra , affine lie algebra , geometry , current algebra , philosophy , epistemology

. We consider the structure of the Kac modules V (Λ) for dominant integral doubly atypical weights Λ of the Lie superalgebra s1(2/2). Primitive vectors of V (Λ) are constructed and it is shown that the number of composition factors of V (Λ) for such Λ is in exact agreement with the conjectures of [HKV]. These results are used to show that the extended Kac‐Weyl character formula which was proved in [VHKTl] for singly atypical simple modules of s1( m/n ), and conjectured to be valid for all finite dimensional irreducible representations of sl( m/n ) in [VHKT2] is in fact valid for all finite‐dimensional doubly atypical simple modules of s1(2/2).

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