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

Brundan, Jonathan

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

Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra $\mathfrak {gl}(m|n)$
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by Jonathan Brundan

J. Amer. Math. Soc. 16 (2003), 185-231

DOI: https://doi.org/10.1090/S0894-0347-02-00408-3

Published electronically: October 16, 2002

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Abstract:

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 $\mathfrak {gl}(\infty )$.

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