Semiinfinite symmetric powers

Abstract

We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate vector space V. Recall that it is obtained as a certain double inductive limit of the exterior algebras of finite-dimensional subquotients of V. (b) The construction of the space of measures on a nonarchimedean local field K with maximal ideal M as a double projective limit of the spaces of measures (=functions) on finite subquotients M^i/M^j of K.

23 pages, AMSTex

Cited by in corpus (9)

• Theta functions and arithmetic quotients of loop groups
• Infinite-dimensional vector bundles in algebraic geometry (an introduction)
• Central extensions and reciprocity laws on algebraic surfaces
• Representations of Higher Adelic Groups and Arithmetic
• Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields
• Higher Tate central extensions via K-theory and infinity-topos theory
• Central extensions and Riemann-Roch theorem on algebraic surfaces
• Geometric class field theory and Cartier duality
• LCA(2), Weil index, and product formula