Cycles in the chamber homology for SL(2,F)

Authors

  • Wemedh Aeal

Keywords:

Local Langlands, Base change, K-theory, Chamber Homology, Baum-Conns map, representation theory, Non-commutative Geometry, Number Theory.

Abstract

We emphasized finding the explicit cycles in the chamber homology groups and the K-theory groups in term of each representation for SL(2,F). This led to an explicit computing of chamber homology and the K-theory groups. We have identified the base change effect on each of these cycles. The base change map on the homology group level works by sending a generator of the homology group of SL(2,E) labeled by a character of E× to the generator of the homology group of SL(2,F) labeled by a character of F× multiplied by the residue field degree. Whilst, it works by sending the K-theory group generator of the reduceC∗-algebraofSL(2,E)labeledbythe1-cycle(resp. 0-cycle)tothemultiplicationoftheresiduefield degree with a generator of the K-theory group of SL(2,F) labeled by the base changed effect on 1-cycle (resp. 0-cycle). 

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Published

2014-01-29

Issue

Section

Algebraic Topology

How to Cite

Cycles in the chamber homology for SL(2,F). (2014). European Journal of Pure and Applied Mathematics, 7(1), 45-54. https://www.ejpam.com/index.php/ejpam/article/view/2013