Search results for "Spin group"
showing 3 items of 3 documents
Norms of harmonic projection operators on compact Lie groups
1988
In order to simplify the notation, we will assume throughout that G is connected, simply connected and semisimple. Sharp estimates for vp(z 0 when G = SU(2) have been obtained by Sogge [6], who proved that Vp(Zt) ~ d~ tl/v), where y(t) is the function which is affine on [1/2, 3/4] and on [3/4, 1] and is such that 7(1/2)=0, 7(3/4)=1/4, 7(1)=1. Two results in the literature give crucial estimates from below for vp(n) in the general case. The first estimate concernes the LP'-norm of the character X, : if ,~, is the highest weight of n and 0 is half the sum of the positive roots, then II x=llp,--> + 011-dimG/p" (1.2)
Spinor algebras
2000
We consider supersymmetry algebras in space-times with arbitrary signature and minimal number of spinor generators. The interrelation between super Poincar\'e and super conformal algebras is elucidated. Minimal super conformal algebras are seen to have as bosonic part a classical semimisimple algebra naturally associated to the spin group. This algebra, the Spin$(s,t)$-algebra, depends both on the dimension and on the signature of space time. We also consider maximal super conformal algebras, which are classified by the orthosymplectic algebras.
A spinorial decomposition of gl_4(R)
2010
We determine six invariant subspaces of the 16-dimensional space gl_4(R) under the conjugation by any element in Spin_3(R). Four of them add up to the 10-dimensional space of symmetric matrices and the other two add up to the 6-dimensional space of skew-symmetric matrices.