Representations by spinor genera

SPINOR GENERA UNDER Zp-EXTENSIONS

Let L be a quadratic lattice over a number field F . We lift the lattice L along a Zp-extension of F and investigate the growth of the number of spinor genera in the genus of L. Let Ln be the lattice obtained from L by extending scalars to the n-th layer of the Zp-extension. We show that, under various conditions on L and F , the number of spinor genera in the genus of Ln is 2 +O(1) where η is ...

Average Representation Numbers for Spinor Genera

In this paper we establish a formula for the average of representation numbers of ternary quadratic forms in a spinor genus over a totally real number field.

Invariant spinor representations of finite rotation matrices

Scalarproducts of Spinor Field Functionals and State Representations in Nonlinear Spinor Field Quantum Theory

In preceding papers it was shown that in nonlinear spinor theory cross-sections of elementary particle scattering processes can be calculated only if the state representations and their scalar products are explicitly known. To obtain these quantities, functional quantum theory of the nonlinear spinor field was introducedIn this paper it is demonstrated that the introduction of functional scalar...

Spin Representations and Centralizer Algebras for the Spinor Groups

We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space ∆ ⊗⊗ k V . Here ∆ is the fundamental representation of Pin(N) and V is the natural (vector) representation of the orthogonal group O(N). We consider the centralizer algebra CPk = EndPin(N)(∆ ⊗⊗k V ) for Pin(N), the double covering group of O(N) and define...