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

Abstract

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 $\mathfrak{q}(n)$.

arXiv commentVersion 2: some minor corrections and updated references

References in corpus (3)

• q-Deformed Fock spaces and modular representations of spin symmetric groups
• $q$-Wedge Modules for Quantized Enveloping Algebras of Classical Type
• Tilting modules for Lie superalgebras

Cited by in corpus (8)

• Stability patterns in representation theory
• Irreducible Characters of General Linear Superalgebra and Super Duality
• Equivalence of blocks for the general linear Lie superalgebra
• Superspace conformal field theory
• A BGG-type resolution for tensor modules over general linear superalgebra
• The primitive spectrum of basic classical Lie superalgebras
• Dual canonical bases, quantum shuffles and q-characters
• On polynomial representations of classical strange Lie superalgebras