4,694 research outputs found
Linear semigroups with coarsely dense orbits
Let be a finitely generated abelian semigroup of invertible linear
operators on a finite dimensional real or complex vector space . We show
that every coarsely dense orbit of is actually dense in . More
generally, if the orbit contains a coarsely dense subset of some open cone
in then the closure of the orbit contains the closure of . In the
complex case the orbit is then actually dense in . For the real case we give
precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page
A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models
The algebraic definition of charges for symmetry-preserving D-branes in
Wess-Zumino-Witten models is shown to coincide with the geometric definition,
for all simple Lie groups. The charge group for such branes is computed from
the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark
Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n
The aim of this work is to study the quotient ring R_n of the ring
Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous
quasi-symmetric functions. We prove here that the dimension of R_n is given by
C_n, the n-th Catalan number. This is also the dimension of the space SH_n of
super-covariant polynomials, that is defined as the orthogonal complement of
J_n with respect to a given scalar product. We construct a basis for R_n whose
elements are naturally indexed by Dyck paths. This allows us to understand the
Hilbert series of SH_n in terms of number of Dyck paths with a given number of
factors.Comment: LaTeX, 3 figures, 12 page
On Motives Associated to Graph Polynomials
The appearance of multiple zeta values in anomalous dimensions and
-functions of renormalizable quantum field theories has given evidence
towards a motivic interpretation of these renormalization group functions. In
this paper we start to hunt the motive, restricting our attention to a subclass
of graphs in four dimensional scalar field theory which give scheme independent
contributions to the above functions.Comment: 54
Berry phase in homogeneous K\"ahler manifolds with linear Hamiltonians
We study the total (dynamical plus geometrical (Berry)) phase of cyclic
quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H,
which can be considered as the phase spaces of classical systems and which are,
in particular cases, coadjoint orbits of some Lie groups G. When the
Hamiltonian is linear in the generators of a Lie group, both phases can be
calculated exactly in terms of {\em classical} objects. In particular, the
geometric phase is given by the symplectic area enclosed by the (purely
classical) motion in the space of coherent states.Comment: LaTeX fil
Twisting algebras using non-commutative torsors
Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can
be used to twist comodule algebras. After surveying and extending the
literature on the subject, we prove a theorem that affords a presentation by
generators and relations for the algebras obtained by such twisting. We give a
number of examples, including new constructions of the quantum affine spaces
and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised.
Sections 1 and 2 were thoroughly restructured. The presentation theorem in
Section 3 is now put in a more general framework and has a more general
formulation. Section 4 was shortened. All examples (quantum affine spaces and
tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are
left unchange
Arbitrarily large families of spaces of the same volume
In any connected non-compact semi-simple Lie group without factors locally
isomorphic to SL_2(R), there can be only finitely many lattices (up to
isomorphism) of a given covolume. We show that there exist arbitrarily large
families of pairwise non-isomorphic arithmetic lattices of the same covolume.
We construct these lattices with the help of Bruhat-Tits theory, using Prasad's
volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde
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