The symplectic Verlinde algebras and string K-theory

Details The symplectic Verlinde algebras and string K-theory The symplectic Verlinde algebras and string K-theory

2009-01-14

arxiv.org/abs/0901.2109v1

Mathematics

Algebraic Topology

38 pages

Scientific paper

We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing the twisted K-theory of the loop spaces of quaternionic projective spaces in detail. Via the work of Freed-Hopkins-Teleman, these computations are related to completions of the Verlinde algebras of Sp(n). We compute these completions, and other relevant information about the Verlinde algebras. We also identify the completions with the twisted K-theory of the Gruher-Salvatore pro-spectra. Further comments on the field theoretic nature of these constructions are made.

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