We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ngô reductive groups. In characteristic p>2, we also weaker statement. 0, the implies that categorical quotient of commuting scheme diagonal adjoint action group is integral normal. As applications, deduce some trace identities certain multiplicative property Pfaffian over an arb...

We construct a well-defined regularized path integral for Lorentzian quantum gravity in terms of dynamically triangulated causal space-times. Each Lorentzian geometry and its action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time and, for finite lattice volume, the associated transfer matrix is self-adjoint, ...

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the N =1 and generalized N =2 supersymmetry theory which leads to the Seiberg-W...

We derive properties of N-extended G R super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification with the spectrum of fields in supergravity theories and superstringrM-theory constructed from NSR N-extended supersymmetric G R Virasoro algebras. q 2000 El...

n An), and |a| ∈ Z denotes the grading. The bracket and differential are required to respect the grading, in that for homogeneous elements, |[a, b]| = |a| + |b| while |∂a| = |a| − 1. The adjoint action of A on itself is given by ade(a) = [e, a] and acts on the grading by ade : An−→An+|e|. In this notation (2) and (3) can be rewritten as • (2) (Jacobi identity) ad[a,b] = [ada, adb] • (3) (Leibni...

Using the action of the Yang–Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall–Littlewood polynomials are a subfamily of one of them. For q = 0, these bases specialize to the two families of classical Key polynomials (i.e., Demazure characters for type A). We give a scalar product for which the two bases are adjoint to each other.

Inspired by a possible relation between large N gauge theory and string theory, we search for nontrivial fixed points in largeN gauge theory in more than four dimensions. We study large N gauge theory through Monte Carlo simulation of the twisted EguchiKawai model in six dimensions as well as in four dimensions. The phase diagram of the system with the two coupling constants which correspond to...