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