Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T04:22:57.055Z Has data issue: false hasContentIssue false

Grassmannian Trilogarithms

Published online by Cambridge University Press:  04 December 2007

A. B. Goncharov
Affiliation:
Department of Mathematics, Brown University, RI 02912, U.S.A.
J. Zhao
Affiliation:
Department of Mathematics, University of Pennsylvania, PA 19104, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the previous works of the first author, two completely different constructions of single valued Grassmannian trilogarithms were given. One of the constructions, in Math. Res. Lett. 2 (1995), 99–114, is very simple and provides Grassmannian n-logarithms for all n. However its motivic nature is hidden. The other construction in Adv. in Math. 114 (1995), 197–318, is very explicit and motivic, but the generalization for n>4 is not known. In this paper we will compute explicitly the Grassmannian trilogarithm constructed in Math. Res. Lett. 2 (1995), 99–114 and prove that it differs from the motivic Grassmannian trilogarithm by an explicitly given product of logarithms. We also derive some general results about the Grassmannian polylogarithms.

Type
Research Article
Copyright
© 2001 Kluwer Academic Publishers