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The next meeting of the Algebra and Logic Seminar will be held in hybrid format in Room 578 of IMI – BAS and online via Zoom on January 8, 2024 (Monday) at 1:00 pm (UTC+2).

A talk on:

On the exceptional series and its siblings

will be delivered by

Bruce Westbury (retired from University of Warwick, UK).


The exceptional series is the following series of eight simple Lie algebras:

A1, A2, G2, D4, F4, E6, E7, E8

Consider each Lie algebra, g, as a representation of the group Aut(g). Then the centraliser algebras of the first five tensor powers of g have common structure. First, they have the same branching rules. We introduce a parameter so that the exceptional series is a set of eight points on a line. Then the values of the quadratic Casimir are linear functions of this parameter and the dimensions are rational functions of this parameter.

The exceptional series is one row in the Freudenthal magic square and all the preferred representations for each row also have analogous common structure. These series are lines. I will give a broad context for this common structure.

There is a plane which contains the first and fourth rows of the magic square and a three-dimensional space which contains the Vogel plane.

Link to the Zoom room:


Algebra and Logic Department, IMI – BAS
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