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
Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C
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
Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$
The character formula of any finite dimensional irreducible module $L_\lambda$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module
Representations of the General Linear Lie Superalgebra in the BGG Category \(\mathcal{O}\)
This is a survey of some recent developments in the highest weight repesentation theory of the general linear Lie superalgebra \(\mathfrak{g}\mathfrak{l}_{n\vert m}(\mathbb{C})\). The main focus is
Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras
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
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 $D(2|1;\zeta)$
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
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
Character and dimension formulae for general linear superalgebra
Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases
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
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
Modular representations of the supergroup Q(n), I
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)
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
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
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
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
...
...