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Grassmannian Trilogarithms

Published online by Cambridge University Press:  04 December 2007

A. B. Goncharov  and
J. Zhao
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.
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Abstract

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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.

Keywords

Polylogarithmsmotivic complexes
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 1 , May 2001 , pp. 83 - 108
Copyright
© 2001 Kluwer Academic Publishers