The SL(2,K) action on a tree, its decomposition and higher dimensional generalisations

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• Vincenzo Di Bartolo, University of Cambridge
• Friday 02 December 2022, 15:00-16:00
• CMS MR13.

If you have a question about this talk, please contact Tom Adams.

For K a non Archimedean local field, it is known (Ihara) that SL(2,K) decomposes as an amalgam of two copies of SL(2,O_K), and this can be shown by letting the group act on a tree of 2-dimentional lattices up to homothety. A natural question arises: can we decompose SL(n,K) (with n>2) in a similar fashion by letting the group act on a similarly constructed higher dimensional simplicial complex? In this talk, I will present a sketch of the proof of Ihara’s result and start to answer the question related to higher dimensions.

This talk is part of the Junior Algebra and Number Theory seminar series.

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