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

@article{Brundan2002KazhdanLusztigPA,
title={Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)},
author={Jonathan Brundan},
journal={arXiv: Representation Theory},
year={2002}
}
• J. Brundan
• Published 1 March 2002
• Mathematics
• arXiv: Representation Theory
206 Citations
Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C
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For the BGG category of $${{\mathfrak{q}}(n)}$$q(n)-modules of half-integer weights, a Kazhdan–Lusztig conjecture à la Brundan is formulated in terms of categorical canonical basis of the nth tensor
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Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras
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We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $${\mathfrak{q}(n)}$$q(n). It is given in terms of the
The Primitive Spectrum of a Basic Classical Lie Superalgebra
We prove Conjecture 5.7 in Coulembier and Musson (Math. J., arXiv:1409.2532), describing all inclusions between primitive ideals for the general linear superalgebra in terms of the $${{\rm Serre functors for Lie algebras and superalgebras • Mathematics • 2010 We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category \mathcal{O} associated to a semi-simple complex finite dimensional Lie algebra. We further Character formulae in category \mathcal O for exceptional Lie superalgebras D(2|1;\zeta) • Mathematics • 2017 We establish character formulae for representations of the one-parameter family of simple Lie superalgebras D(2|1;\zeta). We provide a complete description of the Verma flag multiplicities of the Super duality and Kazhdan-Lusztig polynomials • Mathematics • 2004 We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases • Mathematics • 2013 Let g be an exceptional Lie superalgebra, and let p be the maximal parabolic subalgebra which contains the distinguished Borel subalgebra and has a purely even Levi subalgebra. For any parabolic ## References SHOWING 1-10 OF 119 REFERENCES Kazhdan-Lusztig polynomials and canonical basis • Mathematics • 1997 AbstractIn this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the groupSn coincide with the coefficients of the canonical basis innth tensor THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS  \mathfrak{Gl}(n,\,m) AND  Q(n) Let be the tensor algebra of the identity representation of the Lie superalgebras in the series and . The method of Weyl is used to construct a correspondence between the irreducible representations Generic representations of classical Lie superalgebras and their localization We complete the study of arbitrary generic irreducible modules over a classical complex Lie superalgebraG initiated in [14] (whereG was assumed to be of type I) by presenting a full description of Character formulas for irreducible modules of the Lie superalgebras sl(m/n) • Mathematics • 1990 Kac distinguished between typical and atypical finite‐dimensional irreducible representations of the Lie superalgebras sl(m/n) and provided an explicit character formula appropriate to all the Hecke algebras at roots of unity and crystal bases of quantum affine algebras • Mathematics • 1996 AbstractWe present a fast algorithm for computing the global crystal basis of the basic$$U_q (\widehat{\mathfrak{s}\mathfrak{l}}_n ) -module. This algorithm is based on combinatorial techniques
Categories of Finite Dimensional Weight Modules over Type I Classical Lie Superalgebras
Since the generalization of highest weight representation theory to Lie w x w x superalgebras in K1 ] K3 , a number of interesting results on the highest weight representation theory of classical Lie
Kazhdan-Lusztig conjecture and holonomic systems
• Mathematics
• 1981
In [7], D. Kazhdan and G. Lusztig gave a conjecture on the multiplicity of simple modules which appear in a Jordan-H61der series of the Verma modules. This multiplicity is described in the terms of
Diagram and superfield techniques in the classical superalgebras
• Mathematics
• 1981
Introduces the concept of 'graded permutation group' in the analysis of tensor operators in the classical superalgebras. For U(m/n) and SU(m/n), irreducible tensor representations correspond to