The symplectic Verlinde algebras and string K-theory

Igor Kriz; Joshua T. Levin; Craig Westerland

doi:10.1112/jtopol/jtq029

The symplectic Verlinde algebras and string K-theory

Igor Kriz, Joshua T. Levin, Craig Westerland

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing K_z.ast;^τ(LHP^ℓ) CMMI6.-1.lscript) 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.

Original language	English (US)
Article number	jtq029
Pages (from-to)	901-936
Number of pages	36
Journal	Journal of Topology
Volume	3
Issue number	4
DOIs	https://doi.org/10.1112/jtopol/jtq029
State	Published - 2010

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10.1112/jtopol/jtq029

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abstract = "We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing Kz.ast;τ(LHPℓ) CMMI6.-1.lscript) 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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AB - We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing Kz.ast;τ(LHPℓ) CMMI6.-1.lscript) 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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The symplectic Verlinde algebras and string K-theory

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