Related papers: A Wonderful Embedding of the Loop Group

New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for…

The results of this thesis allows one to replace calculations in tricategories with equivalent calculations in Gray categories (aka semistrict tricategories). In particular the rewriting calculus for Gray categories as used for example by…

There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8, 6.11. These errors have been corrected in the present version of this paper. There are also some minor changes in the introduction.

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

The abstract will be added in due course.

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.

Some mistaken reasonings at the end of the paper omitted.

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

Extensive rewrite. Tables and proofs have been reformatted and/or rewritten for clarity.

A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.

The result in theorem 2.1 has been strengthened (see theorem 2.3) and the remarks in the introduction and the text adapted to this new result. Also some misprints in the previous version have been corrected.

We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative)…

We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the…

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

In the revised version of the paper, we correct misprints and add some new statements.

This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…

This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.