Journal ArticleDOI
A Class of Nonunitary, Finite Dimensional Representations of the Euclidean Algebra 𝔢(2)
Andrew Douglas,Alejandra Premat +1 more
Reads0
Chats0
TLDR
In this paper, the authors examined the finite dimensional representations of the Euclidean algebra 𝔢(2) that are obtained by embedding embeddings into the Lie algebra of traceless 3 × 3 matrices.Abstract:
In this article, we examine the finite dimensional representations of the Euclidean algebra 𝔢(2) that are obtained by embedding 𝔢(2) into 𝔰𝔩3, the Lie algebra of traceless 3 × 3 matrices. We show that the finite dimensional, irreducible representations of 𝔰𝔩3 restricted to 𝔢(2) are indecomposable and, when possible, we give graphical descriptions of these 𝔢(2) representations.read more
Citations
More filters
Journal ArticleDOI
Indecomposable representations of the Diamond Lie algebra
TL;DR: In this paper, the authors study classes of indecomposable representations of the diamond Lie algebra, which is the central extension of the Poincare Lie algebra in two dimensions.
Journal ArticleDOI
The classification of uniserial sl(2)⋉V(m)-modules and a new interpretation of the Racah–Wigner 6j-symbol
TL;DR: The main family of uniserial g-modules for the perfect Lie algebra g = s ⋉ V ( μ ), where s is a semisimple Lie algebra and V( μ ) is the irreducible s -module with highest weight μ ≠ 0, was introduced in this paper.
Journal ArticleDOI
Some nonunitary, indecomposable representations of the Euclidean algebra \mathfrak {e}(3)
Andrew Douglas,Hubert de Guise +1 more
TL;DR: The Euclidean group E(3) is the noncompact, semidirect product group of the Lie group of orientation-preserving isometries of 3D space as discussed by the authors.
Journal ArticleDOI
Embeddings of the Euclidean algebra e(3) into sl(4,C) and restrictions of irreducible representations of sl(4,C)
Andrew Douglas,Joe Repka +1 more
TL;DR: The Euclidean group E(3) is the Lie group of orientation-preserving isometries of three-dimensional space as discussed by the authors, which is the non-compact, semidirect product group of E( 3 ).
Journal ArticleDOI
Indecomposable representations of the euclidean algebra (3) from irreducible representations of
Andrew Douglas,Joe Repka +1 more
TL;DR: The Euclidean group E (3) is the noncompact, semidirect product group of E(3)≅ℝ 3 ⋊SO(3), and it is the Lie group of orientation-preserving isometries of three-dimensional Euclideans.
References
More filters
Journal ArticleDOI
Cones, crystals, and patterns
TL;DR: In this paper, the authors generalize the concept of patterns to arbitrary complex semi-simple algebraic groups, using the path model and the theory of crystals, and show how to use the Young tableaux and the Gelfand-Tsetlin patterns.
Book
Complex Semisimple Lie Algebras
TL;DR: In this paper, the Cartan Subalgebra associated with a regular element and the Weyl Group are discussed.I Nilpotent Lie Algebra and Solvable Lie Algebras (general theorems).
Journal ArticleDOI
Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras
TL;DR: In this article, a generalization of the Littlewood-Richardson rule for Lie algebras by use of crystal base is presented, which describes explicitly the decomposition of tensor products of given representations.
Journal ArticleDOI
Some finite dimensional indecomposable representations of E(2)
Joe Repka,Hubert de Guise +1 more
TL;DR: In this paper, the authors describe the construction of finite dimensional nonunitary representations of E(2), the Lie group of Euclidean transformations in the plane, with emphasis on indecomposable representations.
Related Papers (5)
Indecomposable representations of the Diamond Lie algebra
Some nonunitary, indecomposable representations of the Euclidean algebra \mathfrak {e}(3)
Andrew Douglas,Hubert de Guise +1 more