Tables
Tables of data
Structure and representation-theoretic data for real groups, most of it computed with the atlas software.
Tables
- Unipotent representations of real exceptional groups
Complete list of unipotent representations of real exceptional groups: text files for G2, F4, E6, E7 and E8.
- Structure theory
Tables of structure of Lie groups, computed using the atlas software.
- Representations
Tables of representations computed using the atlas software, including Kazhdan–Lusztig polynomials.
- Spherical unitary representations
The spherical unitary dual of split p-adic exceptional groups: data from John Stembridge and from Dan Barbasch and Dan Ciubotaru.
- Unipotent orbits
Unipotent orbits for exceptional groups: versions of the famous tables from Carter’s and Spaltenstein’s books.
- Models of Weyl group representations
Models of representations of Weyl groups, integral and rational seminormal.
- Galois cohomology
Galois cohomology of simply connected groups: |H1(Γ,G)| for every real form.
From the archive
Older tables and pages
- Unipotent representations and stable sums
Even special unipotent representations of exceptional groups, with cells, orbits and stable sums. Mostly, but not entirely, supplanted by the complete list above.
- Stable sums of unipotent representations
Stable sums at singular infinitesimal character, with pictures of the cell and orbit graphs.
- Computing the unitary dual
The early main page of the unitary dual computations: Weyl group models, spherical representations and structure theory.
- Coxeter
Fokko du Cloux’s program for Coxeter groups, Bruhat order and Kazhdan–Lusztig polynomials (archived pages).
- The E8 root system
The picture of the root system of E8, projected from 8 dimensions down to 2.