Semiinfinite symmetric powers

2001/07/12 by Mikhail Kapranov, M. Kapranov, Kapranov, M. · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Mathematical and Theoretical Analysis #Quantum Algebra (math.QA) #advanced mathematical theories #math.QA

paper · pdf · doi:10.48550/arxiv.math/0107089

23 pages, AMSTex

arxiv created 2001/07/12 · openalex publication_date 2001/07/12 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Mⁱ/M^j of K.

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• Infinite-Dimensional Vector Bundles in Algebraic Geometry

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