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We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra ĝ≠A(2k, 2l)(4). We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.

On a Generic Verma Module at the Critical Level Over Affine Lie Superalgebras