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Integral homology of loop groups via Langlands dual groups

Yun, Zhiwei and Zhu, Xinwen (2011) Integral homology of loop groups via Langlands dual groups. Representation Theory, 15 . pp. 347-369. ISSN 1088-4165.

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Let K be a connected compact Lie group, and G its complexification. The homology of the based loop group ΩK with integer coefficients is naturally a Z-Hopf algebra. After possibly inverting 2 or 3, we identify H∗(ΩK, Z) with the Hopf algebra of algebraic functions on B∨ e , where B^∨ is a Borel subgroup of the Langlands dual group scheme G^∨ of G and B^∨ e is the centralizer in B^∨ of a regular nilpotent element e ∈ LieB^∨. We also give a similar interpretation for the equivariant homology of ΩK under the maximal torus action.

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Additional Information:© Copyright 2011 American Mathematical Society The copyright for this article reverts to public domain 28 years after publication. Received by the editors September 29, 2009 and, in revised form, October 24, 2010. The research of Z.Y. is supported by the National Science Foundation under the agreement No. DMS-0635607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The research of X.Z. was partially conducted during the period he was employed by the Clay Mathematics Institute as a Liftoff Fellow.
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Clay Mathematics InstituteUNSPECIFIED
Classification Code:2010 Mathematics Subject Classification. Primary 57T10, 20G07
Record Number:CaltechAUTHORS:20140919-152325268
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49872
Deposited By: George Porter
Deposited On:23 Sep 2014 04:06
Last Modified:03 Oct 2019 07:18

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