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

Caroline Gruson (1) , Vera Serganova (2)

1 IECN - Institut Élie Cartan de Nancy
2 LBNL - Lawrence Berkeley National Laboratory [Berkeley]

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.

Domaines: Théorie des représentations [math.RT]

Caroline Gruson, Vera Serganova. Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras. Proceedings of the London Mathematical Society, 2010, 101 (3), pp.552-592. ⟨hal-00498493⟩