Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the r...

Consider a field k of characteristic zero. Let Q = (qij) be a n× n-matrix with the entries qij ∈ k∗ or qij is an indeterminate, satisfying qijqji = qii = 1. The algebra k[Q] is generated by k and q ij , i, j = 1, . . . , n. Denote k(Q) = Fract(k[Q]) and Γ is the subgroup in k(Q) generated by k and the entries of Q. Throughout the paper R is a k-algebra with a unit. Definition 1.1. We say that R...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type b A n?1. We give two constructions of this algebra. The rst construction realizes the algebra as a certain endomorphism algebra arising from an aane Hecke algebra of type b A r?1 , where n r. This generalizes the original q-Schur algebra as deened by Dipper and James, and the new algebra contains the ordinary ...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type A n−1. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of type A r−1 , where n ≥ r. This generalizes the original q-Schur algebra as defined by Dipper and James, and the new algebra contains the ordina...