572 research outputs found
Octonionic Representations of GL(8,R) and GL(4,C)
Octonionic algebra being nonassociative is difficult to manipulate. We
introduce left-right octonionic barred operators which enable us to reproduce
the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an
interesting connection between the structure of left-right octonionic barred
operators and generic 4x4 complex matrices. As an application we give an
octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted
Hyperconvex representations and exponential growth
Let be a real algebraic semi-simple Lie group and be the
fundamental group of a compact negatively curved manifold. In this article we
study the limit cone, introduced by Benoist, and the growth indicator function,
introduced by Quint, for a class of representations
admitting a equivariant map from to the Furstenberg boundary
of 's symmetric space together with a transversality condition. We then
study how these objects vary with the representation
A lattice in more than two Kac--Moody groups is arithmetic
Let be an irreducible lattice in a product of n infinite irreducible
complete Kac-Moody groups of simply laced type over finite fields. We show that
if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic
group over a local field and is an arithmetic lattice. This relies on
the following alternative which is satisfied by any irreducible lattice
provided n is at least 2: either is an S-arithmetic (hence linear)
group, or it is not residually finite. In that case, it is even virtually
simple when the ground field is large enough.
More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther
Magic Supergravities, N= 8 and Black Hole Composites
We present explicit U-duality invariants for the R, C, Q, O$ (real, complex,
quaternionic and octonionic) magic supergravities in four and five dimensions
using complex forms with a reality condition. From these invariants we derive
an explicit entropy function and corresponding stabilization equations which we
use to exhibit stationary multi-center 1/2 BPS solutions of these N=2 d=4
theories, starting with the octonionic one with E_{7(-25)} duality symmetry. We
generalize to stationary 1/8 BPS multicenter solutions of N=8, d=4
supergravity, using the consistent truncation to the quaternionic magic N=2
supergravity. We present a general solution of non-BPS attractor equations of
the STU truncation of magic models. We finish with a discussion of the
BPS-non-BPS relations and attractors in N=2 versus N= 5, 6, 8.Comment: 33 pages, references added plus brief outline at end of introductio
Convex Rank Tests and Semigraphoids
Convex rank tests are partitions of the symmetric group which have desirable
geometric properties. The statistical tests defined by such partitions involve
counting all permutations in the equivalence classes. Each class consists of
the linear extensions of a partially ordered set specified by data. Our methods
refine existing rank tests of non-parametric statistics, such as the sign test
and the runs test, and are useful for exploratory analysis of ordinal data. We
establish a bijection between convex rank tests and probabilistic conditional
independence structures known as semigraphoids. The subclass of submodular rank
tests is derived from faces of the cone of submodular functions, or from
Minkowski summands of the permutohedron. We enumerate all small instances of
such rank tests. Of particular interest are graphical tests, which correspond
to both graphical models and to graph associahedra
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
The shortwave infrared bands response to stomatal conductance in Conference" Pear Trees (Pyrus communis L.)"
Published: 8 October 201
Parameters for Twisted Representations
The study of Hermitian forms on a real reductive group gives rise, in the
unequal rank case, to a new class of Kazhdan-Lusztig-Vogan polynomials. These
are associated with an outer automorphism of , and are related to
representations of the extended group . These polynomials were
defined geometrically by Lusztig and Vogan in "Quasisplit Hecke Algebras and
Symmetric Spaces", Duke Math. J. 163 (2014), 983--1034. In order to use their
results to compute the polynomials, one needs to describe explicitly the
extension of representations to the extended group. This paper analyzes these
extensions, and thereby gives a complete algorithm for computing the
polynomials. This algorithm is being implemented in the Atlas of Lie Groups and
Representations software
The Center Conjecture for spherical buildings of types F4 and E6
We prove that a convex subcomplex of a spherical building of type F4 or E6 is
a subbuilding or the automorphisms of the subcomplex fix a point on it. Our
approach is differential-geometric and based on the theory of metric spaces
with curvature bounded above. We use these techniques also to give another
proof of the same result for the spherical buildings of classical type.Comment: 34 pages. An intrinsic version of the results has been added. Proof
of the Center Conjecture for spherical buildings of classical types added.
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