We introduce the notion of a straight tableau and prove that the straight tableaux of xed row-convex shape form a basis for the GL n -representations and the general linear Lie superalgebra representations associated to the given shape. We provide a straightening algorithm for expressing arbitrary tableaux in terms of straight tableaux. These techniques can be modi ed to provide bases for repre...

Under fairly general conditions, we extend the 5-sequence of cohomology for nilpotent Lie algebras a step further. We then derive some consequences of the construction.

A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...

Making use of a Howe duality involving the infinite-dimensional Lie superalgebra ĝl∞|∞ and the finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of ĝl∞|∞ in terms of hook Schur functions. We use the reduction procedure of ĝl∞|∞ to ĝln|n to derive a character formula for a certain class of level 1 highest weight ir...

Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...