22,499 research outputs found
Factor equivalence of Galois modules and regulator constants
We compare two approaches to the study of Galois module structures: on the
one hand factor equivalence, a technique that has been used by Fr\"ohlich and
others to investigate the Galois module structure of rings of integers of
number fields and of their unit groups, and on the other hand regulator
constants, a set of invariants attached to integral group representations by
Dokchitser and Dokchitser, and used by the author, among others, to study
Galois module structures. We show that the two approaches are in fact closely
related, and interpret results arising from these two approaches in terms of
each other. We also use this comparison to derive a factorisability result on
higher -groups of rings of integers, which is a direct analogue of a theorem
of de Smit on -units.Comment: Minor corrections and some more details added in proofs; 11 pages.
Final version to appear in Int. J. Number Theor
Musical Thought And Compositionality
Many philosophers and music theorists have claimed that music is a language, though whether this is meant metaphorically or literally is often unclear. If the claim is meant literally, then it faces serious difficultyâmany find it compelling to think that music cannot be a language because it lacks any semantic value. On the other hand, if it is meant metaphorically, then it is not clear what is gained by the metaphorâit is not clear what the metaphor is meant to illuminate. Considering the claim as a metaphor, I take it that what a theorist who speaks in this way is trying to draw our attention to is that there are interesting and illuminating parallels between music and language that might be philosophicallysignificant. Ifthisistheirpoint,thenthequestionis:whatinteresting parallel is it that could be so philosophically significant
GCM study of hexadecapole correlations in superdeformed Hg
The role of hexadecapole correlations in the lowest superdeformed band of
Hg is studied by self consistent mean field methods. The generator
coordinate method with particle number projection has been applied using
Hartree-Fock wave functions defined along three different hexadecapole paths.
In all cases, the ground state is not significantly affected by hexadecapole
correlations and the energies of the corresponding first excited hexadecapole
vibrational states lie high in energy. The effect of rotation is investigated
with the Skyrme-Hartree-Fock-Bogolyubov method and a zero range
density-dependent pairing interaction.Comment: REVTeX file, 10 pages, 3 figures (available as postscript files upon
request to [email protected]), submitted to Phys. Rev.
Mean-Field Description of Fusion Barriers with Skyrme's Interaction
Fusion barriers are determined in the framework of the Skyrme energy-density
functional together with the semi-classical approach known as the Extended
Thomas-Fermi method. The barriers obtained in this way with the Skyrme
interaction SkM* turn out to be close to those generated by phenomenological
models like those using the proximity potentials. It is also shown that the
location and the structure of the fusion barrier in the vicinity of its maximum
and beyond can be quite accurately described by a simple analytical form
depending only on the masses and the relative isospin of target and projectile
nucleus.Comment: 7 pages, latex, 5 figure
Relations between permutation representations in positive characteristic
Given a finite group G and a field F, a G-set X gives rise to an
F[G]-permutation module F[X]. This defines a map from the Burnside ring of G to
its representation ring over F. It is an old problem in representation theory,
with wide-ranging applications in algebra, number theory, and geometry, to give
explicit generators of the kernel K_F(G) of this map, i.e. to classify pairs of
G-sets X, Y such that F[X] is isomorphic to F[Y]. When F has characteristic 0,
a complete description of K_F(G) is now known. In this paper, we give a similar
description of K_F(G) when F is a field of characteristic p>0 in all but the
most complicated case, which is when G has a subquotient that is a
non-p-hypo-elementary (p,p)-Dress group.Comment: 18 pages; minor corrections and improvements. Final version to appear
in Bull. London Math. So
Brauer relations in finite groups
If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise
to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map
from the Burnside ring to the representation ring of G has a kernel. Its
elements are called Brauer relations, and the purpose of this paper is to
classify them in all finite groups, extending the Tornehave-Bouc classification
in the case of p-groups.Comment: 39 pages; final versio
Torsion homology and regulators of isospectral manifolds
Given a finite group G, a G-covering of closed Riemannian manifolds, and a
so-called G-relation, a construction of Sunada produces a pair of manifolds M_1
and M_2 that are strongly isospectral. Such manifolds have the same dimension
and the same volume, and their rational homology groups are isomorphic. We
investigate the relationship between their integral homology. The
Cheeger-Mueller Theorem implies that a certain product of orders of torsion
homology and of regulators for M_1 agrees with that for M_2. We exhibit a
connection between the torsion in the integral homology of M_1 and M_2 on the
one hand, and the G-module structure of integral homology of the covering
manifold on the other, by interpreting the quotients Reg_i(M_1)/Reg_i(M_2)
representation theoretically. Further, we prove that the p-primary torsion in
the homology of M_1 is isomorphic to that of M_2 for all primes p not dividing
#G. For p <= 71, we give examples of pairs of isospectral hyperbolic
3-manifolds for which the p-torsion homology differs, and we conjecture such
examples to exist for all primes p.Comment: 21 pages; minor changes; included a data file; to appear in J.
Topolog
Nuclear Mean Fields through Selfconsistent Semiclassical Calculations
Semiclassical expansions derived in the framework of the Extended
Thomas-Fermi approach for the kinetic energy density tau(r) and the spin-orbit
density J(r) as functions of the local density rho(r) are used to determine the
central nuclear potentials V_n(r) and V_p(r) of the neutron and proton
distribution for effective interactions of the Skyrme type. We demonstrate that
the convergence of the resulting semiclassical expansions for these potentials
is fast and that they reproduce quite accurately the corresponding Hartree-Fock
average fields.Comment: LATEX, 25 pages, including 11 eps figures. to be published in Europ.
Phys. Journal
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