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Published March 2008 | Submitted
Journal Article Open

New Deformations of Group Algebras of Coxeter Groups, II

Abstract

This paper is a sequel of [ER]. Specifically, let W be a Coxeter group, generated by s_i, i ∈ I. Then, following [ER], one can define a new deformation A_+ = A_+(W) of the group algebra Z[W_+] of the group W_+ of even elements in W. This deformation is an algebra over the ring R = Z[t^(±1)_(ijk)] = Z[T] of regular functions on a certain torus T of deformation parameters. The main result of [ER] implies that this deformation is flat (i.e. A_+ is a flat R-module) if and only if for every triple of indices Δ = {i, j, k} ⊂ I the corresponding rank 3 parabolic subgroup WΔ ⊂ W is infinite. (To be more precise, in [ER] we work over C, but the results routinely extend to the case of ground ring Z.)

Additional Information

© 2008 Birkhaeuser. Received: May 2006; Accepted: July 2007; First Online: 30 January 2008. It is our pleasure to dedicate this paper to Joseph Bernstein. His work, as well as style of doing and explaining mathematics, have been an inspiration for generations of mathematicians. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. E.R. was supported in part by NSF grant DMS-0401387. The authors would also like to acknowledge that at many stages of this work they used the MAGMA package for algebraic computations [M].

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August 19, 2023
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