## Tables of Representation Theory

The tables contain the output of the atlas
software package, of the following commands

- blocksizes: list of sizes of blocks for G
- kgb: the K-orbits on G/B
- block: list of representations in a block
- kllist: list of distinct Kazhdan-Lusztig of the block
- klbasis: list of all non-zero P_{gamma,nu} of the block
- wcells: normalized cells of the W-graph of the block
- wgraph: W-graph of the block

The directory structure is precise, and somewhat elaborate.
For example:

E6: tables for E6

E6/simplyConnected: simply connected complex group

E6/simplyConnected/splitInnerClass: groups in this inner class (split and K=F4)

/tables/representations/E6/adjoint/splitInnerClass/split/dualT1D5:
block of representations of simply connected split group E6, dual to (adjoint) Hermitian symmetric group
(with K=T1D5)
In each hiearchy are files **blocksizes** and **kgb**
at the appropriate level.

For example, for the block of the simply connected split group of type E6, dual to T1D5 (Hermitian symmetric):

E6/simplyConnected/splitInnerClass/blocksizes for the sizes of the blocks

E6/simplyConnected/splitInnerClass/split/kgb
for the K\G/B orbits

E6/simplyConnected/splitInnerClass/split/dualT1D5/block

Tables of representation theory for type:

A1 (complete)

B2 (complete)

E6 (complete)

E7 (complete)

E8 (partial)

Send corrections to jda@math.umd.edu

Tables of structure theory

Computing the Unitary Dual
Atlas Home Page