Let F be the underlying base field of characteristic p > 3 and denote by W and S the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras W and S. Using certain properties of the canonical tori of W and S, we then determine the derivation algebra of W and the derivation spa...

We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie’s theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected ...

An explicit character formula is established for any strongly generic finite-dimensional irreducible g-module, g being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl cha...

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined representation of a conformal Lie (super)algebra L is completely determined by commutation relations of L and by the requirement of associative locality of generators. W...

Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra based weight system. Le and Murakami showed that these two link invariants are the same. These constructions can be generalized to some classes of Lie super...

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...

A Fock space is introduced which admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal tilting and irreducible characters for the Lie superalgebra osp(2|2n). We also determine all the composition factors for the symmetric tensors of the natural osp...

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...

The algebraic cohoroology and the spectral sequences for a Z2-graded Lie algebra are briefly reviewed. The reducibility property of a strongly semisiiaple Lie superalgebra is established. The role of second and third cohomologies in the deformation of a Lie superalgebra is discussed. Using spectral sequences, the second cohomology of full BRS algebra is shown to be W and the third cohomology be...