## 206 Citations

Character Formulae for Queer Lie Superalgebras and Canonical Bases of Types A/C

- Mathematics
- 2015

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 $\mathfrak{osp}(n|2)$

- Mathematics
- 2009

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 \(\mathcal{O}\)

- Mathematics
- 2014

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

- Mathematics
- 2015

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

- Mathematics
- 2016

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)$

- Mathematics
- 1985

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

- Mathematics
- 1994

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

- Mathematics
- 1996

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…