Cell modules for the Temperley—Lieb algebra in mixed characteristic

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• Charles Senecal, University of Cambridge
• Wednesday 05 March 2025, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

Introduced in the 1970s, the family of Temperley—Lieb algebras TL_n have since appeared in many different areas of representation theory, from lattice models in statistical physics to categorification of Hecke algebras in the theory of Soergel bimodules. While their representation theory in characteristic zero has been well understood for some time, the situation over a field of positive characteristic is much more intricate. After an introduction to Temperley—Lieb diagrams and to the language of cellular algebras, we will describe recent results about the structure of the so-called cell modules for TL_n in the mixed characteristic case, making an explicit use of TL_n’s rôle in the Schur—Weyl duality for quantum sl_2 along the way. This is joint work with S. Martin and R. Spencer.

This talk is part of the Algebra and Representation Theory Seminar series.

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