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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On constructions of Lax representations: some examples
松弛表示 构造 非线性数学物理方程 KdV方程
2023/1/6
著名数学家Peter Lax 在1968年将重要的非线性数学物理方程---KdV方程表示为一个算子方程， 即给出了KdV方程的Lax表示或Lax对。Lax对在孤立子理论的发展中扮演者重要角色，可以看成是研究可积系统的出发点。但如何构造一个给定非线性系统的Lax表示却是非常困难的问题。本报告在概述Lax表示历史的基础上，以Boris Kupershmidt提出的两个非线性发展型方程为具体例子，介绍L...
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
2015/9/29
Goldman gratefully acknowledges partial support by NSF grants
DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research
Award from the General Research Board of the University of
Maryland in Fa...
Sensitivity experiments to mountain representations in spectral models
spectral models mountain representations
2015/9/28
This paper describes a set of sensitivity experiments to several formulations of orography. Three sets are considered: a "Standard" orography consisting of an envelope orography produced originally fo...
Vector coherent state representations and their inner products
Vector coherent state representations their inner products Mathematical Physics
2012/6/30
Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Repre...
On a class of tensor product representations for the orthosymplectic superalgebra
orthosymplectic algebra tensor product complete reducibility maximal vector
2012/5/1
We introduce the spinor representations for osp(m|2n). These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup ...
Embedded Representations and Quasi-Dynamical Symmetry
Embedded Representations Quasi-Dynamical Symmetry
2011/7/20
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more real...
Unitary representations of the Galilean line group: Quantum mechanical principle of equivalence
Unitary representations the Galilean line group Quantum mechanical principle of equivalence
2011/7/13
Abstract: We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on...
Semidirect Product of Groupoids, Its Representations and Random Operators
Semidirect Product of Groupoids Representations Random Operators
2011/7/9
Abstract: One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidire...
Categories of unitary representations of Banach-Lie supergroups and restriction functors
Banach–Lie supergroups unitary representations smooth vectors analytic vectors
2011/7/5
Abstract: We prove that the categories of smooth and analytic unitary representations of Banach--Lie supergroups are well-behaved under restriction functors, in the sense that the restriction of a rep...
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
Hurwitz zeta function Riemann zeta function Dirichlet L function generalized Bernoulli number
2011/6/25
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant.
Hypergeometric summation representations of the Stieltjes constants
Riemann zeta function Stieltjes constants generalized hypergeometric function
2011/6/25
Hypergeometric summation representations of the Stieltjes constants.
W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
W-extended Kac representations integrable boundary conditions the logarithmic minimal models
2011/6/24
W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p).
Representations of the Dirac wave function in a curved spacetime
the Dirac wave function curved spacetime
2010/11/30
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a c...
Irreducible Highest Weight Representations Of The Simple n-Lie Algebra
Irreducible Highest Weight Representations Simple n-Lie Algebra
2010/11/30
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of ...
On non-local representations of the ageing algebra
On non-local representations the ageing algebra
2010/11/30
The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z=2. Here, new representations for an integer dynamical exponent z=n are co...