computing character degrees via a galois connection

Computing Character Degrees via a Galois Connection

In a previous paper, the second author established that, given finite fields F < E and certain subgroups C ≤ E×, there is a Galois connection between the intermediate field lattice {L | F ≤ L ≤ E} and C’s subgroup lattice. Based on the Galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product C⋊Gal(E/F ). However, the analysis when |F | i...

A Galois Connection for Reduced Incidence Algebras

If (V = j 1, • • • , n |, D CN x N, and F is an equivalence relation on the "entries" of D the reduced incidence space g(f ) is the set of all real matrices A with support in D and such that a.. = a whenrr ij rs ever (i, j)F(r, s). Let S(D) be the lattice of all subspaces of R having support contained in D, and S(D) that of all equivalences on D. Then the map g defined above is Galois connected...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

On Finite Groups With Two Irreducible Character Degrees

Computing Science AN ALGEBRAIC THEORY OF COMPLEXITY FOR VALUED CONSTRAINTS: ESTABLISHING A GALOIS CONNECTION

The complexity of any optimisation problem depends critically on the form of the objective function. Valued constraint satisfaction problems are discrete optimisation problems where the function to be minimised is given as a sum of cost functions defined on specified subsets of variables. These cost functions are chosen from some fixed set of available cost functions, known as a valued constrai...

Galois connection for multiple-output operations

It is a classical result from universal algebra that the notions of polymorphisms and invariants provide a Galois connection between suitably closed classes (clones) of finitary operations f : B n → B, and classes (coclones) of relations r ⊆ B k. We will present a generalization of this duality to classes of (multi-valued, partial) functions f : B n → B m , employing invariants valued in partia...