We use the Fock space representation of the quantum affine algebra of type A (2) 2n to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture relating this basis to decomposition matrices of spin symmetric groups in characteristic 2n + 1.

In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an α-Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σ ◦ F is a α-Lipschitz function. The Lipschitz operators algebras Lα(K,A) and lα(K,A) are developed here further, and we st...

The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...

Let K be an arbitrary field of characteristic p > 0 and D(Pn) the ring of differential operators on a polynomial algebra Pn in n variables. A long anticipated analogue of the inequality of Bernstein is proved for the ring D(Pn). In fact, three different proofs are given of this inequality (two of which are essentially characteristic free): the first one is based on the concept of the filter dim...

Let K be an arbitrary field of characteristic p > 0 and D(Pn) be the ring of differential operators on a polynomial algebra Pn in n variables. A long anticipated analogue of the inequality of Bernstein is proved for the ring D(Pn). In fact, three different proofs are given of this inequality (two of which are essentially characteristic free): the first one is based on the concept of the filter ...

The configuration of regular 3-forms in dimension 6 is generalized to n-forms in dimension 2n. The algebras of complex, paracomplex, and dual numbers are systematically used. The automorphism groups of all forms are determined. In the last decade there has arisen interest in exterior forms of higher degree, first of all in forms of degree 3 (see [2] and [3]). It is known (see [4] and [1]) that ...

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...