Glenn Lancaster

Representation-functors and flag-algebras for the classical groups I

i.e., to the ring R[G/U] of regular R-valued functions on the variety G/U, where U is the unipotent radical of any Bore1 subgroup of 6. Moreover, this construction is given explicitly by generators and relations, where this presentation has the property that it is a ‘“Z-form” of the flag-algebra R[G/U], i.e., not only does R[G/lJ] have generators (yi}iel and relations on these, given by the presentation, with the coefficients of these relations in Z, but also these relations generate, over Z, all relations on the (y,> with coefficients in Z. The algebra-valued functor A + is naturally graded, the gr~ding~mono~ consisting of partitions (i.e., finite unordered sequences of integers, repetitions permitted), with the monoid-operation union of partitions. Each “graded piece” Aa is a functor from R-modules to R-modules, with a presentation, given by the above construction, which is a “Z-form,” in the above sense, of a suitable irreducible representation of Gk(n); all nonzero irreducible polynomial representations of GL(M) arise exactly once in this way. These functors A’, and their analogs for the other classical groups to be described below, are the “representation-functors” in the title of [6] and of the present article; the Aa have been called “Schur functors” and ‘“shape functors”; the authors believe that [S] is the first appearance of these AE in the literature. They have recently proved useful tools in certain algebraic applications involving free resolutions. In [6], the present authors extended this work to the groups SO(21-t I) 265 0021-8693185

An improved articulated model of the human hand

3.00