Fermionic construction of the Z2\frac{\mathbb{Z}}{2}-graded meromorphic open-string vertex algebra and its Z2\mathbb{Z}_2-twisted module, I

We define the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra that is an appropriate noncommutative generalization of the vertex operator superalgebra. We also illustrate an example that can be viewed as a noncommutative generalization of the free fermion vertex operator superalgebra. The example is bulit upon a universal half-integer-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators. The former feature allows us to define the normal ordering, while the latter feature allows us to describe interactions among the fermions. With respect to the normal ordering, Wick's theorem holds and leads to a proof of weak associativity and a closed formula of correlation functions.Comment: 37 pages. Comments and suggestions are welcome

Finite group actions on reductive groups and buildings and tamely-ramified descent in Bruhat-Tits theory

The purpose of the paper is to give a new approach to tamely-ramified descent in Bruhat-Tits theory. This descent was first studied by Guy Rousseau in his thesis.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1611.0743