Decomposition Numbers of SL3(pn) and SU3(pn)

✍ Scribed by Leonard Chastkofsky

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 156 KB
• Volume: 240
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8723

✦ Synopsis

We review the results obtained in 1 , as applied to SL p and 3

Ž n . Let ⌫ be either the group SL p or SU p . Let X be the weight n 3 3 lattice for ⌫ . It is isomorphic to ‫ޚ‬ q = ‫ޚ‬ q . Let X n be the subset of n p p n -restricted weights, consisting of those elements of X whose coordinates in terms of the fundamental dominant weights lie between 0 and p n y 1.

The projective indecomposable characters are indexed by weights in X n . Let ⌽ be the projective indecomposable character indexed by .

p , n

Let W be the Weyl group. Let W be the affine Weyl group, that is, a, p the semidirect product of W with translations by elements of p times the