Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra 𝔤𝔩(𝔪|𝔫)

Brundan, Jonathan ¹

¹ Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Journal of the American Mathematical Society, Tome 16 (2003) no. 1, pp. 185-231

Résumé

We compute the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak {gl}(m|n)$, and determine ${\operatorname {Ext}}$’s between simple modules in the category of finite dimensional representations. We formulate conjectures for the analogous results in category $\mathcal O$. The combinatorics parallels the combinatorics of certain canonical bases over the Lie algebra $\mathfrak {gl}(\infty )$.

Détail

DOI : 10.1090/S0894-0347-02-00408-3

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