Howe dualities lead to diagrammatic categories which describe the representations of Lie-type objects as a monoidal category (that is, via generators and relations). Applying this philosophy type Q duality Cheng–Wang Sergeev, we introduce web supercategories relations show they full subcategory supermodules for Lie superalgebra given by tensor products supersymmetric powers natural supermodule.

In our recent paper [DSK11] we computed the dimension of the variational Poisson cohomology H•K(V) for any quasiconstant coefficient l × l matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the Z-graded Lie sup...

In our recent paper [DSK11] we computed the dimension of the variational Poisson cohomology H•K(V) for any quasiconstant coefficient l × l matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the Z-graded Lie sup...

Here we describe a Gauss decomposition of the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y (A(m− 1, n− 1)) defined and studied in papers by Stukopin. We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian Y (glm|n). This is a conjecture of Nazaro...

We introduce the marked Brauer algebra and the marked Brauer category. These generalize the analogous constructions for the ordinary Brauer algebra to the setting of a homogeneous bilinear form on a Z2-graded vector space. We classify the simple modules of the marked Brauer algebra over any field of characteristic not two. Under suitable assumptions we show that the marked Brauer algebra is in ...

We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra D(1)(2, 1;x). Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck’s analysis uses heavily the (extended) affine Weyl groups of the affine Lie algebras. In our approach the structures are based on a Weyl groupoid. Preprint numbers: MIT-CTP 38...

We consider a class of Lie superalgebra, called spinc supersym-metry algebras, constructed from spinor representation. They are motivated by supersymmetry algebras used by physicists. On a Riemannian manifold, a KK ahler manifold, and a hyperkk ahler manifold respectively, it is known that some natural operators on the space of diierential forms span spinc (2), spinc(3) and spinc (5) supersymme...

Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g ⊕ g+, and let s and t be commuting formal variables commuting with g. We prove that the map C : sg[[s, t]] × tg+[[s, t]] −→ sg[[s, t]] ⊕ tg+[[s, t]] defined by the Campbell-Baker-Hausdorff formula and given by e − e + = eC(sg ,tg) for g ∈ g[[s, t]] is a bijection, as is well known when g ...