Results 321 to 330 of about 1,803,467 (337)

Construction of invariants for simple lie groups

Nuclear Physics, 1964
Abstract A coupling coefficient for the orthogonal and symplectic groups is defined.It can be utilized to construct a set of invariants and it is proved that these are all the independent invariants of the considered groups excepting the orthogonal group in even dimensions for which an invariant cannot be constructed in a similar way.
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Graded modules over classical simple Lie algebras with a grading

, 2013
Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules.
A. Elduque, M. Kochetov
semanticscholar   +1 more source

Group Structure of Gauge Theories: Hermitian irreducible representations of compact simple Lie algebras

, 1986
Preface Part I. Group Structure: 1. Global properties of groups and Lie groups 2. Local properties of Lie groups 3. Lie algebras 4. Hermitian irreducible representations of compact simple Lie algebras 5.
L. O'Raifeartaigh
semanticscholar   +1 more source

Branching Rules for Simple Lie Groups

Journal of Mathematical Physics, 1965
If Γ is an irreducible representation of a group 𝒢, and ℋ is a subgroup of 𝒢, then Γ furnishes a representation of ℋ which is, in general, reducible, and the branching rules specify which irreducible representations of ℋ occur in the decomposition of this representation.
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Simple Lie Groups of Rank One [PDF]

, 2001
Let X be a rank one Riemannian symmetric space of the noncompact type, and G be the group of isometries of X. There are four cases: (1) X is real n-hyperbolic space (n ≥ 2) and G = SO0 (n, 1); (2) X is complex n-hyperbolic space (n ≥ 2) and G = SU(n, 1); (3) Xis quaternionic n-hyperbolic space (n ≥ 2) and G = Sp(n, 1);
openaire   +1 more source

The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups

Monatshefte f�r Mathematik, 2002
Let \(G\) be a semisimple Lie group with finite center and \(S\subseteq G\) a subsemigroup with non-empty interior. The authors show that if \(S\) is generated by one-parameter semigroups, then there exists a compact subgroup of \(G\) whose homotopy groups are precisely the homotopy groups of \(S\).
Alexandre J. Santana, Luiz A. B. San Martin   +1 more
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Characters of Semi-Simple Lie Groups

1967
Let C be the circle group, that is, the multiplicative group of all complex numbers c with |c| = 1. Then for every integer n, we have the character χn of C given by χn(c) = cn, and these are the only (irreducible) characters of C. Moreover, the main result in the theory of Fourier series asserts that $$f(1) = \sum\limits_{ - \infty < n < \infty } \;
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Simple Groups and Simple Lie Algebras [PDF]

Journal of the London Mathematical Society, 1965
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The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group

, 1959
B. Kostant
semanticscholar   +1 more source

Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one

, 1989
M. Cowling, U. Haagerup
semanticscholar   +1 more source