110 research outputs found
On compression of Bruhat-Tits buildings
We obtain an analog of the compression of angles theorem in symmetric spaces
for Bruhat--Tits buildings of the type .
More precisely, consider a -adic linear space and the set of
all lattices in . The complex distance in is a complete system of
invariants of a pair of points of under the action of the complete
linear group. An element of a Nazarov semigroup is a lattice in the duplicated
linear space . We investigate behavior of the complex distance under
the action of the Nazarov semigroup on the set .Comment: 6 page
Notes on Stein-Sahi representations and some problems of non harmonic analysis
We discuss one natural class of kernels on pseudo-Riemannian symmetric
spaces.Comment: 40p
Stein--Sahi complementary series and their degenerations
The aim of the paper is an introduction to Stein--Sahi complementary series,
holomorphic series, and 'unipotent representations'. We also discuss some open
problems related to these objects. For the sake of simplicity, we consider only
the groups U(n,n).Comment: 40pp, 7fig, revised versio
The vector-valued big q-Jacobi transform
Big -Jacobi functions are eigenfunctions of a second order -difference
operator . We study as an unbounded self-adjoint operator on an
-space of functions on with a discrete measure. We describe
explicitly the spectral decomposition of using an integral transform
with two different big -Jacobi functions as a kernel, and we
construct the inverse of .Comment: 35 pages, corrected an error and typo
A Simple Analytic Solution for Tachyon Condensation
In this paper we present a new and simple analytic solution for tachyon
condensation in open bosonic string field theory. Unlike the B_0 gauge
solution, which requires a carefully regulated discrete sum of wedge states
subtracted against a mysterious "phantom" counter term, this new solution
involves a continuous integral of wedge states, and no regularization or
phantom term is necessary. Moreover, we can evaluate the action and prove Sen's
conjecture in a mere few lines of calculation.Comment: 44 pages
Contractions of Low-Dimensional Lie Algebras
Theoretical background of continuous contractions of finite-dimensional Lie
algebras is rigorously formulated and developed. In particular, known necessary
criteria of contractions are collected and new criteria are proposed. A number
of requisite invariant and semi-invariant quantities are calculated for wide
classes of Lie algebras including all low-dimensional Lie algebras.
An algorithm that allows one to handle one-parametric contractions is
presented and applied to low-dimensional Lie algebras. As a result, all
one-parametric continuous contractions for the both complex and real Lie
algebras of dimensions not greater than four are constructed with intensive
usage of necessary criteria of contractions and with studying correspondence
between real and complex cases.
Levels and co-levels of low-dimensional Lie algebras are discussed in detail.
Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio
Step-Wise Computational Synthesis of Fullerene C60 derivatives. 1.Fluorinated Fullerenes C60F2k
The reactions of fullerene C60 with atomic fluorine have been studied by
unrestricted broken spin-symmetry Hartree-Fock (UBS HF) approach implemented in
semiempirical codes based on AM1 technique. The calculations were focused on a
sequential addition of fluorine atom to the fullerene cage following indication
of the cage atom highest chemical susceptibility that is calculated at each
step. The effectively-non-paired-electron concept of the fullerene atoms
chemical susceptibility lays the foundation of the suggested computational
synthesis. The obtained results are analyzed from energetic, symmetry, and the
composition abundance viewpoints. A good fitting of the data to experimental
findings proves a creative role of the suggested synthesis methodology.Comment: 33 pages, 11 figures, 2 tables, 2 chart
On Deformations of n-Lie algebras
The aim of this paper is to review the deformation theory of -Lie
algebras. We summarize the 1-parameter formal deformation theory and provide a
generalized approach using any unital commutative associative algebra as a
deformation base. Moreover, we discuss degenerations and quantization of
-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin
Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other
author
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
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