Lie algebras of matrix difference differential operators and special matrix functions
نویسندگان
چکیده
منابع مشابه
Classification of Quasifinite Modules over Lie Algebras of Matrix Differential Operators on the Circle
We prove that an irreducible quasifinite module over the central extension of the Lie algebra of N × N -matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate series. Furthermore, we give a complete classification of indecomposable uniformly bounded modules.
متن کاملRepresentations of Matrix Lie Algebras
Building upon the concepts of the matrix Lie group and the matrix Lie algebra, we explore the natural connections between the Lie groups and Lie algebras via the exponential map. We later introduce the matrix commutator as a Lie bracket operation to aid our investigation of Lie algebra representations, which we illustrate with the example of the adjoint representation on the special unitary group.
متن کاملLie Algebras and Lie Brackets of Lie Groups–matrix Groups
The goal of this paper is to study Lie groups, specifically matrix groups. We will begin by introducing two examples: GLn(R) and SLn(R). Then in each section we will prove basic results about our two examples and then generalize these results to general matrix groups.
متن کاملCertain Properties of Some Special Matrix Functions via Lie Algebra
In this paper, we establish a result concerning eigenvector for the product of two operators C and D defined on a Lie algebra of endomorphisms of a vector space. Further, A new method has been devised to define some properties viz. differential recurrence relations and differential equations of 2-variables generalized Hermite matrix polynomials and 2variables matrix Laguerre polynomials to deri...
متن کاملLie Algebras of Differential Operators and Lie-Algebraic Potentials
An explicit characterisation of all second order differential operators on the line which can be written as bilinear combinations of the generators of a linitedimensional Lie algebra of first order differential operators is found, solving a problem arising in the Lie-algebraic approach to scattering theory and molecular dynamics. One-dimensional potentials corresponding to these Lie algebras ar...
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: Advances in Applied Mathematics
سال: 2021
ISSN: 0196-8858
DOI: 10.1016/j.aam.2020.102109