We develop some basic properties such as $p$-centers of affine vertex algebras and free field vertex algebras in prime characteristic. We show that the Wakimoto-Feigin-Frenkel homomorphism preserves… Expand

In this paper, we study Heisenberg vertex algebras over fields of prime characteristic. The new feature is that the Heisenberg vertex algebras are no longer simple unlike in the case of… Expand

The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The… Expand

Proceedings of the National Academy of Sciences of the United States of America

1986

TLDR

An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.Expand

Abstract In the basic representation of[formula]realized via the algebra of symmetric functions, we compare the canonical basis with the basis of Macdonald polynomials where t = q 2 . We show that… Expand