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…