Local wreath product modules

Wreath Product Symmetric Functions

We systematically study wreath product Schur functions and give a combinatorial construction using colored partitions and tableaux. The Pieri rule and the Littlewood-Richardson rule are studied. We also discuss the connection with representations of generalized symmetric groups.

algebra and wreath product convolution

We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...

Scalar Product Graphs of Modules

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...

Image Processing with Wreath Product Groups

Virasoro algebra and wreath product convolution

We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...