Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)

Details Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n) Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)

2002-07-02

arxiv.org/abs/math/0207024v2

Advances Math. 182 (2004), 28-77.

Mathematics

Representation Theory

Version 2: some minor corrections and updated references

Scientific paper

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach relating the character problem to canonical bases of the quantized enveloping algebra $U_q(\mathfrak b_{\infty})$. We also formulate for the first time a conjecture for the characters of the infinite dimensional irreducible representations in the analogue of category $\mathcal O$ for the Lie superalgebra $\mathfrak{q}(n)$.

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