Lifting wreath product extensions

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...

A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup ΣGn associated with G ≀ Sn, the wreath product of the symmetric group Sn with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an anti-homomorphism from the Sn-invariant subalgebra ...

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...