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We use geometrical methods adapted from Borel–Weil–Bott theory to compute the character of every finite‐dimensional simple module over a basic classical Lie superalgebra. The answer is given by a combinatorial algorithm in terms of weight and cap diagrams, which were defined by Brundan and Stroppel for the general linear superalgebra.

Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras