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本文计算了秩为n+1的一类特殊的Verlinde模性范畴l的Casimir数，计算结果表明该Casimir数为2n+4.作为应用，由Higman定理知域K上的Grothendieck代数Gr （l）⊗Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式En+1（X）在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零，借助于Dickso...
CASIMIR OPERATORS AND MONODROMY REPRESENTATIONS OF GENERALISED BRAID GROUPS
CASIMIR OPERATORS MONODROMY REPRESENTATIONS GENERALISED BRAID GROUPS
2015/10/14
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
Singular Casimir Elements Euler Equation Equilibrium Points Analysis of PDEs
2011/10/10
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
the Euler Equation Equilibrium Points Analysis of PDEs
2011/9/21
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
We prove a certain unexpected regularity of geodesic restrictions for the (hyperbolic) Casimir operator. We prove a nontrivial bound on L2-norm of a geodesic restriction for eigenfunctions
of the Cas...
We study the Casimir energy of a scalar field for a regular polygon with N sides.
Casimir energy scalar field regular polygon
2011/2/25
We study the Casimir energy of a scalar field for a regular polygon with N sides.The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon.
Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory
Modal Hamiltonian interpretation of quantum mechanics Casimir operators quantum field theory
2011/3/2
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.
We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give ex...
Casimir函数在广义哈密顿控制系统中的应用
伪Poisson流形 Casimir函数 受控广义哈密顿系统 能量守恒
2012/11/29
首先研究伪Poisson流形的Casimir函数与结构矩阵的关系，给出了伪Poisson流形存在Casimir函数的一个充要条件；然后利用所得结果研究扩张的广义哈密顿系统的构造问题，给出了扩张的广义哈密顿系统存在Casimir函数且保持能量守恒的2个充分条件.