We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute the...

Let G be a finite group with Sylow 2-subgroup P 6 G. Navarro–Tiep–Vallejo have conjectured that the principal 2-block of NG(P) contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible characters in the principal 2-block of G are fixed by a certain Galois automorphism σ. By recent work of Navarro–Vallejo it suffices to show this conjecture holds for al...

Let G be a connected unipotent group over a finite field Fq. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(Fq) and give an explicit description of L-packets in terms of the so-called “admissible pairs” for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension...

In this article we construct an irreducible simple subgroup G = 〈q, y, t, w〉 of GL8671(13) from an irreducible subgroup T of GL11(2) isomorphic to Mathieu’s simple group M24 by means of Algorithm 2.5 of [13]. We also use the first author’s similar construction of Fischer’s sporadic simple group G1 = Fi23 described in [11]. He starts from an irreducible subgroup T1 of GL11(2) contained in T whic...

This paper gives a method for computing values of certain nonabelian Artin ¿-functions in the complex plane. These Artin ¿-functions are attached to irreducible characters of degree 2 of Galois groups of certain normal extensions K of Q. These fields K are the ones for which G = Gal(.KyQ) has an abelian subgroup A of index 2, whose fixed field Q(\/d) is complex, and such that there is a a S G —...

The common zero locus of a set of multivariate polynomials (with complex coefficients) determines an algebraic set. Any algebraic set can be decomposed into a union of irreducible components. Given a one dimensional irreducible component, i.e. a curve, it is useful to understand its invariants. The most important invariants of a curve are the degree, the arithmetic genus and the geometric genus...

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...

Let G be a finite group and Ω a set of n elements. Assume that G acts faithfully on Ω and let V be a vector space over the complex field C, with dimV = m ≥ 2. It is shown that for each irreducible constituent χ of permutation character of G, the symmetry class of tensors associated with G and χ is non-trivial. This extends a result of Merris and Rashid (see [6, Theorem 2]).