Search results for "Fundamental representation"

Simple and semisimple Lie algebras and codimension growth

1999

Irreducible finitary Lie algebras over fields of positive characteristic

2000

A Lie subalgebra L of [gfr ][lfr ][ ](V) is said to be finitary if it consists of elements of finite rank. We study the situation when L acts irreducibly on the infinite-dimensional vector space V and show: if Char [ ] > 7, then L has a unique minimal ideal I. Moreover I is simple and L/I is solvable.

Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

1998

Abstract A Lie subalgebraLof g l K (V) is said to befinitaryif it consists of elements of finite rank. We show that if Char  K  = 0, if dim K  Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple.

Domain walls in supersymmetric QCD: The taming of the zoo

2000

We provide a unified picture of the domain wall spectrum in supersymmetric QCD with Nc colors and Nf flavors of quarks in the (anti-) fundamental representation. Within the framework of the Veneziano-Yankielowicz-Taylor effective Lagrangian, we consider domain walls connecting chiral symmetry breaking vacua, and we take the quark masses to be degenerate. For Nf/Ncm** there is no domain wall. We numerically determine m* and m** as a function of Nf/Nc, and we find that m** approaches a constant value in the limit that this ratio goes to one.

Initial state azimuthal anisotropies in small collision systems

2015

Strong multiparticle azimuthal correlations have recently been observed in high energy proton-nucleus collisions. While final state collective effects can be responsible for many of the observations, the domain structure in the classical color field of a high energy nucleus also naturally leads to such correlations. We describe recent calculations of the momentum space 2-particle cumulant azimuthal anisotropy coefficients v_n{2}, n=2,3,4 from fundamental representation Wilson line distributions describing the high energy nucleus. We find significant differences between Wilson lines from the MV model and from JIMWLK evolution. We also discuss the relation of this calculation to earlier work …

Singular quadratic Lie superalgebras

2012

In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.

Non linear representations of Lie Groups

1977

International audience

Separation of unitary representations of connected Lie groups by their moment sets

2005

AbstractWe show that every unitary representation π of a connected Lie group G is characterized up to quasi-equivalence by its complete moment set.Moreover, irreducible unitary representations π of G are characterized by their moment sets.