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This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Toda Lattices Continuum Limit Random Matrices Odd Weights
2011/7/7
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/28
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Bounds for coefficients of cusp forms and extremal lattices
coefficients of cusp forms extremal lattices
2011/3/1
A cusp form f(z) of weight k for SL2(Z) is determined uniquely by its first ℓ := dim Sk Fourier coefficients. We derive an explicit bound on the nth coefficient of f in terms of its first ℓ...
Zeta-functions of weight lattices of compact semisimple connected Lie groups
Zeta-functions compact semisimple connected Lie groups
2010/11/8
We define zeta-functions of weight lattices of compact semisimple connected Lie groups. If the group is simply-connected, these zeta-functions coincide with ordinary zeta-functions of root systems of ...
We extend the theory of spinor class field and representation fields previously defined for lattices over the ring of integers of a number field to both, lattices over the coordinate ring of a smooth ...
Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
strong solidity lattices
2010/12/3
We show that the group factors L, where is an ICC lattice in either SO(n, 1)or SU(n, 1), n ≥ 2, are strongly solid in the sense of Ozawa and Popa [13]. This strengthens a result o...
Infinite generation of non-cocompact lattices on right-angled buildings
Infinite generation non-cocompact lattices right-angled buildings
2010/12/9
Let be a non-cocompact lattice on a locally finite regular right-angled building X. We prove that if has a strict fundamental domain then is not finitely generated. We...
In [13], K¨otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space.
Modular and lower-modular elements of lattices of semigroup varieties
Semigroup variety lattice of varieties commutative variety
2010/12/3
The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the varie...
Sachs [16] showed that a Boolean algebra is determined by its lattice of subalgebras.We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determin...
We introduce the concept of quasi-hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi-hyperalgebraic. Some ch...