Radial Part Calculations for $\widehat {\mathfrak {sl}}_2$ and the Heun-KZB Heat Equation
نویسندگان
چکیده
منابع مشابه
Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$
Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal affine Lie subalgebras, and highest weight modules are described under the condition $c_1>0$ and $c_2=0$.
متن کاملHeun Equation and Painlevé Equation
We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.
متن کاملOn the Heun equation.
A new approach to the theory of finite-gap integration for the Heun equation is constructed. As an application, global monodromies of the Heun equation are calculated and expressed as hyperelliptic integrals. The relationship between the Heun equation and the spectral problem for the BC1 Inozemtsev model is also discussed.
متن کاملAn efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...
متن کاملHeun Equation and Inozemtsev Models
The BCN elliptic Inozemtsev model is a quantum integrable systems with N -particles whose potential is given by elliptic functions. Eigenstates and eigenvalues of this model are investigated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2015
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnv064